DOCSLIB.ORG

Resolving the Two-Dimensional ANNNI Model Using Transfer Matrices

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Resolving the Two-Dimensional ANNNI Model Using Transfer Matrices Resolving the two-dimensional ANNNI model using transfer matrices Yi Hu1 and Patrick Charbonneau1, 2, ∗ 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA 2Department of Physics, Duke University, Durham, North Carolina 27708, USA (Dated: December 18, 2020) The phase diagram of the two-dimensional ANNNI model has long been theoretically debated. Extremely long structural correlations and relaxation times further result in numerical simulations making contradictory predictions. Here, we introduce a numerical transfer matrix treatment that bypasses these problems, and thus overcome various ambiguities in the phase diagram. In particular, we confirm the transition temperatures and clarify the order of the transition to the floating incom- mensurate phase. Our approach motivates considering transfer matrices for resolving long-standing problems in related statistical physics models. I. INTRODUCTION matrix (TM) approach should be able to resolve all of these issues.29,30 This approach indeed provides ex- act solutions of semi-infinite systems, which can then Patterned and modulated phases robustly form when be extrapolated to the thermodynamic limit by finite- the components of a system interact via competing short- size scaling. Because both computational and memory range attractive and long-range repulsive (SALR) inter- complexity grow exponentially with system size, how- actions.1{4 Such phases have indeed been observed in ever, the accessible size range has long been too nar- materials ranging from magnetic alloys,5,6 to lipidic sur- row for physical insight to emerge from such an analy- factants,7,8 and biological tissues.9,10 Frustration, how- sis. Thanks to dramatic improvements in methodology, ever, is also associated with slowly decaying finite-size computer hardware and eigensolvers31 the TM approach corrections and to complex relaxation processes, which has recently been applied to more complex (quasi) one- both severely impede the study of equilibrium phases by dimensional continuum-space systems, including SALR numerical simulations. Specialized sampling techniques models with up to third-nearest-neighbor interaction,32 are thus needed to study even minimal microphase- and hard spheres in cylindrical confinement up to next- formers,11{14 let along more realistic ones. nearest-neighbor interaction.33{35 For two-dimensional Lattice models with SALR interactions were first for- lattice models with frustration, sufficiently large sys- mulated forty years ago, the simplest being the ax- tems have also recently become accessible to the TM 15 ial next-nearest-neighbor Ising (ANNNI) model. Yet approach to determine transition temperatures on the re- even in two dimensions, this small perturbation to the 36 lated J1−J2 model. In this article, we push the effective Ising model makes an analytical solution out of reach. use of the TM formalism to resolve various physical am- Different approximation methods have thus been at- biguities of the somewhat more complex ANNNI model. 16 tempted, including Hamiltonian limit, free fermion ap- In particular, we determine the phase boundaries for the 17 18 proximation, high temperature series expansion, clus- floating IC phase, and critically assess proposals for the 19 20,21 ter variational method and others. Although the Lifshitz point and the IC phase reentrance. physics of both the small frustration regime and the en- ergetic ground states have long been resolved, the finite temperature-strong frustration regime has not. Between II. TRANSFER MATRIX APPROACH the standard high-temperature paramagnetic phase and low-temperature modulated antiphase, a floating incom- The ANNNI model Hamiltonian for spin variables s = mensurate (IC) phase intercalates. From field-theory, i ±1 reads this critical phase is expected to be of the Kosterlitz- Thouless (KT) type, and thus to belong to the XY uni- X X X HANNNI = −J1 sisj + J2 sisj − J0 si; (1) versality class.22,23 Numerical validation, however, has hi;ji [i;j] i remained elusive, as has whether the IC phase persists axial 21 at large frustrations or disappears at a Lifshitz point. where the coupling constant J = J1 > 0, the frus- arXiv:2012.09747v1 [cond-mat.stat-mech] 17 Dec 2020 Both high and low transition temperatures (Tc1 and Tc2, tration along the axial next-nearest-neighbor direction respectively) are indeed challenging to determine in sim- κ = J2=J1 > 0 and the external field h = J0=J are 12,24{28 ulations (see Ref. 12). The proposed reentrance scaled. For κ = 0, the model reduces to the standard 19,20 of the IC phase around the multiphase point also Ising model; for the T = 0 ground state, ferromagnetic remains to be confirmed. Because these features are cen- order dominates until κ < 1=2, and the periodic an- tral to our understanding of the floating IC phase in mi- tiphase (with periodicity h2i) takes overs for κ > 1=2. crophase formers, resolving these questions is particularly Note that in lattice-gas representation, this model corre- important. sponds to SALR interacting particles, and h then plays As was recognized already in the mid-1980s, a transfer- the role of an effective chemical potential. The ANNNI 2 model is thus clearly a minimal model for layered mi- III. PHASE DIAGRAM FOR h = 0 crophases. The finite-temperature, finite-frustration phase behav- We first consider results from the ?TM route (Fig. 1). ior of semi-infinite strips is obtained by a TM approach For κ < 1=2, the energy curves for different L robustly with each layer s having L spins s1; s2; :::; sL. (Setting cross at well-defined critical point Tc(κ). For the Ising, sL+1 ≡ s1 imposes periodic boundary conditions.) Be- 39,40 κ = 0, limit u(Tc) is perfectly invariant with L, while cause the interaction in the ANNNI model is anisotropic, for 0 < κ 1=2, small systems, L 10, exhibit a correc- 29 . the TM can be propagated either perpendicular (?TM) tion of at most 0:1%. From this identification of T (κ) 30 c or parallel (kTM) to the axial next-nearest-neighbor in- we confirm that the peak of c grows logarithmically with teraction direction. Both matrices can be decomposed L, as expected for the Ising universality class. into intra-layer, T , and inter-layer, T , contributions, x y For κ & 1=2 a markedly different behavior is observed. 27 1 1 A pronounced step in u(T ) gives rise to a sharp c peak. 2 2 T = Tx TyTx : (2) At first glance, these features might suggest a simple first- order transition, in contrast to the Pokrovsky-Talapov In TM, row and column indices correspond to neigh- ? scenario,24 but the single step height scales as 1=L (not boring layer configurations s and s0, shown) and is thus projected to vanish in the thermody- 8 h i namic, 1=L ! 0, limit. Furthermore, a second peak ap- T (s) = exp J PL (s s − κs s + hs ) ; <? x i=1 i i+1 i i+2 i pears for L ≥ 24, a third one for L ≥ 32, and it is reason- 0 PL 0 :?Ty(s; s ) = exp J i=1 sisi ; able to expect that more such peaks eventually do. This (3) behavior is related to the stepwise change to the modula- L L tion block Nmod from the h2i antiphase (Fig. 1(c)). This which makes ?T a 2 × 2 symmetric dense matrix. In TM, row and column indices correspond to two subse- change in modulation has long been considered a finite- k size echo of the thermodynamic floating IC phase.41 quent layers fs; s0g and fs0; s00g, respectively, and then Although the transition temperatures identified by the step-wise steps and heat capacity peaks shift with L, 8 h i 0 PL 0 finite-size results clearly suggest an exponential scaling, <kTx(s; s ) = exp J (sisi+1 + sisi + hsi) ; i=1 c ∼ exp(aL)=L (up to c ≥ 103) (Fig. 1(d)), and thus a L (4) 00 P 00 42 :kTy(s; s ) = exp −κJ i=1 sisi ; first-order transition. At finite L, the modulation takes up available fractions of the system size, and as 1=L ! 0, L L which makes kT a 4 × 4 non-symmetric sparse matrix infinite commensurate phases are separated by infinites- with 8L nonzero entries. imal temperature intervals. As a result the system re- In both cases the leading eigenvalue, λ0, provides the mains critical everywhere, which is a hallmark of the free energy per spin, f = − log λ0=(βL), and the product floating IC phase. The transition at Tc2 being discontin- of left and right leading eigenvectors, P (s) = '−1(s)'(s), uous (rather than critical), as was proposed in Ref. 27, provides the equilibrium probability of a layer config- is thus here confirmed. Extrapolating the temperature uration. Equilibrium configurations can thus be effi- of the first peak using a quadratic form further gives 37 ciently planted. Thermal properties can be obtained Tc2(κ = 0:6) = 0:90(1), which is fully consistent with the by taking partial derivatives of f, e.g., the energy u = most recent simulations.28 The second lowest transition is 2 −kBT @(βf)=@T and specific heat c = @u=@T per spin. projected to merge with the first as 1=L ! 0. The mod- The leading correlation length can also be obtained from ulation wavenumber q = Nmod=L thus seemingly shifts 0 the spectrum gap, ξ1 = 1= log(λ0=jλ1j), albeit only along from q0 = 1=4 to some q < q0, resulting in an abrupt the direction of layer propagation. Hence, although the change in q at Tc2. Admittedly, the alternative scenario compactness of ?TM brings larger L within computa- that q could non-smoothly yet continuously change at Tc2 tional reach, the kTM geometry is more informative cannot be excluded, but the first-order transition (discon- about the modulation direction, which is of greater phys- tinuity in u) proposal appears marginally more consistent ical interest.
Load more

Recommended publications
  • Information Quarterly for Computer Simulation of Condensed Phases
    ..Jaresbury Laboratory INFORMATION QUARTERLY FOR COMPUTER SIMULATION OF CONDENSED PHASES An informal Newsletter associated with Collaborative Computational Project No.5 on Molecular Dynamics, Monte Carlo & Lattice Simulations of Condensed Phases. Number 35 September 1992 Contents • General News 2 • Registration Form 5 • Post Doctoral Position 6 a Meeting and workshop announcements 6 o Aqueous systems 6 • Polymers in Motion T a THE CCPS PROGRAM LIBRARY. E-mail Service 8 o DLPOLY A Macromolecular Simulation Package 15 W. Smith, C. Dean, D. Fincham, D. Tildesley • CASCADE and THBREL- Implementation on the INTEL iPSC/860 17 C. Dean, M. Leslie, S. E. Marshall and S. C. Parker ' CCPS Literature Survey 1991 20 Editor: Dr. M. Lesley SERC Oaresbury Laboratory Daresbury, Warrington WA4 4AO UK General News FUTURE MEETINGS AND WORKSHOPS A sununary table is given below, further details may be found inside. ,l TOPIC DATES LOCATION ! i AQUEOUS SYSTEMS READING UNI· December 18 109'2 j VERSITY I J CCP5 PROGRAM LIBRARY Details are contained in this issue of accessing the CCP5 program library through E-mail automatically. Also details of accessing the Allen/Tildesley example programs at Cornell are repeated from the last issue. CRAY NEWS As most of our readers are aware, the Atlas Centre now has a Cray Y· MPSI/8128 installed. It Js currently available for trial use. There are 8 pro­ cessors, 1281vl words of memory and 100Gbytes of disk storage. Each processor has about 1.4 times the peak performance of an X-MP processor. CCP5 participants are reminded that CCP5 has an annual allocation of Cray time at Rutherford which will be transferred to the Y-MP_ This is avail­ able for the development of simulation programs which are of general use to the CCPG conununity.
    [Show full text]
  • Quantum Fidelity Approach to the Ground State Properties of the 1D
    Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field O. F. de Alcantara Bonfim∗ Department of Physics, University of Portland, Portland, Oregon 97203, USA B. Boechat† and J. Florencio‡ Departamento de F´ısica, Universidade Federal Fluminense Av. Litorˆanea s/n, Niter´oi, 24210-340, RJ, Brazil In this work we analyze the ground-state properties of the s = 1/2 one-dimensional ANNNI model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field Bx and the strength of the next-nearest-neighbor interaction J2, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, h2, 2i phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L → ∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second-order, whereas the line between the floating and the h2, 2i phases is possibly of first-order. PACS numbers: 75.10.Pq,75.10.Jm I. INTRODUCTION neighbor interactions in the presence of a magnetic field in the transverse direction. The transverse Ising model At very low temperatures, quantum fluctuations play was initially used to explain the order-disorder transi- an important role in the characterization of the ground- tions observed in KDP ferroelectrics [2]. An experimen- state properties of quantum systems [1]. These fluctua- tal realization of that model in real magnetic systems was tions are induced by varying the relative strength of com- observed in LiHoF4 in an external field [3].
    [Show full text]
  • Absence of Long-Range Order in the Frustrated Magnet Srdy2o4 Due to Trapped Defects from a Dimensionality Crossover
    PHYSICAL REVIEW B 95, 134430 (2017) Absence of long-range order in the frustrated magnet SrDy2O4 due to trapped defects from a dimensionality crossover N. Gauthier,1,* A. Fennell,2 B. Prévost,3 A.-C. Uldry,4 B. Delley,4 R. Sibille,2 A. Désilets-Benoit,3 H. A. Dabkowska,5 G. J. Nilsen,6 L.-P. Regnault,6 J. S. White,2 C. Niedermayer,2 V. Pomjakushin,2 A. D. Bianchi,3 and M. Kenzelmann1,† 1Laboratory for Scientific Developments and Novel Materials, Paul Scherrer Institut, 5232 Villigen, Switzerland 2Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen, Switzerland 3Département de Physique & Regroupement Québécois sur les Matériaux de Pointe (RQMP), Université de Montréal, Montréal, Québec H3C 3J7, Canada 4Condensed Matter Theory Group, Paul Scherrer Institut, 5232 Villigen, Switzerland 5Brockhouse Institute for Materials Research, Hamilton, Ontario L8S 4L8, Canada 6Institut Laue-Langevin, CS 20156, F-38042 Grenoble Cedex 9, France (Received 8 February 2017; published 19 April 2017) Magnetic frustration and low dimensionality can prevent long-range magnetic order and lead to exotic 3+ correlated ground states. SrDy2O4 consists of magnetic Dy ions forming magnetically frustrated zigzag chains along the c axis and shows no long-range order to temperatures as low as T = 60 mK. We carried out neutron scattering and ac magnetic susceptibility measurements using powder and single crystals of SrDy2O4. Diffuse neutron scattering indicates strong one-dimensional (1D) magnetic correlations along the chain direction that can be qualitatively accounted for by the axial next-nearest-neighbor Ising model with nearest-neighbor and next-nearest-neighbor exchange J1 = 0.3 meV and J2 = 0.2 meV, respectively.
    [Show full text]
  • Tunable Emergent Heterostructures in a Prototypical Correlated Metal
    Tunable Emergent Heterostructures in a Prototypical Correlated Metal D. M. Fobes,1 S. Zhang,2 S.-Z. Lin,3 Pinaki Das,1,* N. J. Ghimire,1,§ E. D. Bauer,1 J. D. Thompson,1 L.W. Harriger,4 G. Ehlers,5 A. Podlesnyak,5 R.I. Bewley,6 A. Sazonov,7 V. Hutanu,7 F. Ronning,1 C. D. Batista,1, 2 and M. Janoschek1, † 1MPA-CMMS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA 3T-4, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 4NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 5QCMD, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 6ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Chilton, Didcot, Oxon OX11 0QX, United Kingdom 7Institute of Crystallography, RWTH Aachen University and Jülich Centre for NeutronScience (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Lichtenbergstr. 1, D-85747 Garching, Germany *Current address: Division of Materials Sciences and Engineering, Ames Laboratory, U.S. DOE, Iowa State University, Ames, Iowa 50011, USA §Current address: Argonne National Laboratory, Lemont, Illinois 60439, USA †Corresponding author: [email protected] At the interface between two distinct materials desirable properties, such as superconductivity, can be greatly enhanced,1 or entirely new functionalities may emerge.2 Similar to in artificially engineered heterostructures, clean functional interfaces alternatively exist in electronically textured bulk materials. Electronic textures emerge spontaneously due to competing atomic-scale interactions,3 the control of which, would enable a top-down approach for designing tunable intrinsic heterostructures.
    [Show full text]
  • Crystal-Field Symmetry and Ordered Phases in Arrays of Helical Xy Spin Chains
    University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1993 Crystal-Field Symmetry And Ordered Phases In Arrays Of Helical Xy Spin Chains O. Heinonen University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib1990 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 1990s by an authorized administrator of STARS. For more information, please contact [email protected]. Recommended Citation Heinonen, O., "Crystal-Field Symmetry And Ordered Phases In Arrays Of Helical Xy Spin Chains" (1993). Faculty Bibliography 1990s. 719. https://stars.library.ucf.edu/facultybib1990/719 PHYSICAL REVIEW B VOLUME 47, NUMBER 5 1 FEBRUARY 1993-I Crystal-Beld symmetry and ordered phases in arrays of helical XY spin chains O. Heinonen Department of Physics, University of Central Florida, Ortando, Ftorida M816' (Received 21 April 1992; revised manuscript received 21 July 1992) The e8'ect of crystal-field symmetry and strength on the nature of ordered phases in three- dimensional systems consisting of arrays of helical XY spin chains is investigated. The phase diagrams of chiral chains in arrays with twofold symmetry always exhibit a Lifshitz point, where paramagnetic, ferromagnetic, and incommensurate phases meet. In contrast, the phase diagrams of chains in arrays in which the crystal field has higher symmetry than twofold have no Lifshitz point, whether the chains are chiral or not. In these arrays, the initial phase transition is always paramag- netic to incommensurate.
    [Show full text]
  • S^?I V3 MMS& %:-•> '$K*Sf Rx*T>A '£*? M// ^^^Bîhï
    vm •S^?i V3 MMS& %:-•> '$K*Sf rX*T>A '£*? m// ^^^BîHï //.-/w ^' y///. '"—'/^v/Ay//^ v/ 7/'//;y// //y Applications for the use of the ILL facilities All research proposals have to be submitted to the Scientific Commercially exploitable results Council for approval. The Council meets twice each year and the closing dates for the acceptance of applications are: Visitors and ILL scientists may occasionally be involved in ex­ February 15 and August 31. periments which have possible commercial applications. If any The completed research proposal forms should be sent to: scientist considers that this is the case, he should get in touch The Scientific Coordination & Public Relations Of­ with the Scientific Secretary. fice (SCAPRO) Institut Max von Laue — Paul Langevin Other publications available 156 X Neutron Research Facilities at the ILL High Flux Reactor, Edi­ 38042 Grenoble Cedex tion 1983. France Information and Regulations for Reactor Users, Long-Term Tel. (76) 48.72.44 B. Maier Visitors and New Scientific Staff, Edition March 1984 48.71.79 G. Briggs both available from SCAPRO 48.70.41 K. Mayer-Jenkins (Secretary) Experimental Reports and Theory College Activities 1983 48.70.82 A. Taffut (Secretary) available from the ILL Library. Telex: 320621 F (Appropriate application forms may be obtained on request from the above office). Under normal circumstances the ILL makes no charge for the use of its facilities. However, special equipment (other than the existing instruments, counters, standard cryostats and shielding requirements) must be provided by the user. This ap­ plies particularly to the experimental samples which must, in all cases, be provided by the user.
    [Show full text]
  • Modulated Structures in a Lebwohl-Lasher Model with Chiral Interactions Arxiv:1903.01822V2
    Modulated structures in a Lebwohl-Lasher model with chiral interactions E. S. Nascimento∗1, A. Petriy2, and S. R. Salinasz3 1 Depto de F´ısica,PUC-Rio, Rio de Janeiro, RJ, Brazil 2 CNR - Istituto dei Sistemi Complessi, Dipartimento di Fisica, Universit`aSapienza, Roma, Italy 3 Instituto de F´ısica,USP, S~aoPaulo, SP, Brazil Abstract We consider a Lebwohl-Lasher lattice model with nematic directors restricted to point along p planar directions. This XY Lebwohl-Lasher system is the nematic analogue of the standard p-state clock model. We then include chiral interactions, and introduce a chiral p-state nematic clock model. The statistical problem is formulated as a discrete non-linear map on a Cayley tree. The attractors of this map correspond to the physical solutions deep in the interior of the tree. It is possible to observe uniform and periodic structures, depending on temperature and a parameter of chirality. We find many different chiral nematic phases, and point out the effects of temperature and chirality on the modulation associated with these structures. Keywords: Chiral nematics; statistical models; phase behavior; Cayley tree 1 Introduction Competing interactions are the basic mechanism to describe the onset of sequences of modulated phases in many physical systems [1{4]. In magnetism, the most investigated lattice statistical model to account for the existence of spatially modulated structures is the ANNNI model [5{7], which is an Ising system with competing ferro and antiferromag- netic interactions between first and second-neighbor spins along an axial direction. The ANNNI model exhibits one of the richest phase diagrams in the literature, with a wealth arXiv:1903.01822v2 [cond-mat.stat-mech] 25 Jun 2019 of modulated structures depending on temperature and on a parameter associated with the ratio between the strengths of the competing couplings.
    [Show full text]
  • Proceedings of the Joint Nordic Spring Meeting '92
    ?>*«)3>OOOlt>A -j^t DI Risø-R-628(EN) Proceedings of the Joint Nordic Spring Meeting '92 Edited by Per-Anker Lindgård JOINT NORDIC SPRING MEETING 7-10 MAY 1992 Nyborg Strand, Denmark Risø National Laboratory, Roskilde, Denmark May 1992 Proceedings of the Joint Nordic K-*«(BO Spring Meeting '92 Edited by Per-Anker Lindgård Risø National Laboratory, Roskilde, Denmark May 1992 Abstract Proceedings in the form of extended abstracts of the Joint Nordic Spring Meeting '92 including the 3rd Nordic Conference on Surface Science, the Nordic Symposium on Com­ puter Simulation, and 3rd Nordic Symposium on Superconductivity. In addition there are contributions from workshops on the Physics of Small Clusters, on Soft Condensed Matter Physics and from an Electronic Properties Workshop. The proceedings contain over 300 contributions on the mentioned subjects. Further, there are several contributions on general solid state subjects, magnetism, semiconductors etc. ISBN 87-550-1810-6 ISSN 0106-2840 Gransk Service Ris«, 1992 RiM-R-628(EN) THE SOLID STATE SECTIONS OF THE NORDIC PHYSICAL SOCIETIES in cooperation with the 3rd NORDIC CONFERENCE ON SURFACE SCIENCE 6th NORDIC SYMPOSIUM ON COMPUTER SIMULATION 3rd NORDIC SYMPOSIUM ON SUPERCONDUCTIVITY JOINT NORDIC SPRING MEETING 7-10 MAY 1992 Nyborg Strand, Denmark Sponsors: NorFa The Danish Natural Science Research Council NORDITA NOVOs Fond Thomas B.Thrige's Fond Kraks Fond Knud Højgaards Fond Danish Ministry of Research and Education The Materials Development Program (MUP) on: High-Tc Superconducting Thin Film Components The Materials Development Program on: Synchroton Radiation Studies of Surfaces Ri*#-R-62S(EN) 3 ORGANIZING COMMITTEES: Plenum Scientific Committee: Per-Anker Lindgard, Ris«, Denmark (chairman) Henrik Jeldtoft Jensen, NBI, Denmark (secretary) Jens Onsgaard, Odense, Denmark Ole G.
    [Show full text]
  • Models with Competing Interactions
    Models with competing interactions Cristian Micheletti Christ Church Department of Physics, Theoretical Physics University of Oxford Thesis submitted for the degree of Doctor of Philosophy in the University of Oxford Trinity Term 1996 Models with competing interactions Cristian Micheletti Christ Church Department of Physics, Theoretical Physics University of Oxford University of Oxford Abstract We examine the occurrence of spatially modulated structures in several models with competing interactions. Of particular interest are the situations where, for given values of the interactions, the ground-state is infinitely degenerate. Most of the work presented here concerns the analysis of how this zero-temperature multidegeneracy can be removed by the introduction of weak perturbations sush as spin anisotropy, external magnetic fields, or quantum fluctuations. In Chapters 2-4, we consider models of finite or semi-infinite chains of spins, where the competition between surface and bulk effects creates a domain wall (kink) in the ground state. In particular in Chapter 2 we show that, in a chain of ferromagnetically-coupled XY spins with p-fold anisotropy (p ≥ 3), the softening of the spins removes the degeneracy by stabilizing a sequence of layering transitions. It is also argued that, when p = 2, the persistence of multidegeneracy in the classical model can be eliminated by quantum effects. In Chapter 3 the effects of quantum fluctuations on the behaviour of an interface are considered further for the case of the three-dimensional transverse Ising model. Finally we study a chain of antiferromagnetically-coupled XY spins with two-fold anisotropy in an external magnetic field. The analytical and numerical results, presented in Chapter 4, reveal that, in semi-infinite and finite chains of even length, there is a sequence of layering transitions in the bulk that has not been previously identified.
    [Show full text]
  • Phd and Mphil Thesis Classes
    First-principles investigations of ordering in binary alloys Moshiour Rahaman Doctoral thesis School of Industrial Engineering and Management, Department of Materials Science and Engineering, KTH Stockholm, October, 2013 Materialvetenskap KTH SE-100 44 Stockholm Sweden ISBN 978-91-7501-880-5 Akademisk avhandling som med tillst˚andav Kungliga Tekniska H¨ogskolan framl¨agges till offentlig granskning f¨oravl¨aggandeav doktorexamen fredagen den 18 oktober 2013 kl 10:00 i sal B1, Kungliga Tekniska H¨ogskolan, Brinellv¨agen23, Stockholm. c Moshiour Rahaman, October 2013 Tryck: Universitetsservice US AB i Abstract The aim of the thesis is to study ordering in binary alloys on the basis of first- principles or ab-initio techniques employing density functional theory (DFT). The or- dering phenomena of materials are of crucial importance for technological applications. The results of the thesis are intended to demonstrate the applicability of the first- principles calculations to provide fundamental insight to the true, namely electronic structure, nature of ordering in binary alloys. The main part of the thesis focuses on atomic short- and long-range order phenom- ena in binary alloys as a function of both temperature and chemical composition in FeCo and NiCr alloys. In particular, the influence of magnetism on atomic ordering in FeCo alloys is investigated using the disordered local moment. A large number of concentration dependent effective cluster interactions, derived without the use of any adjustable parameters, are obtained by the SGPM as it is implemented in the EMTO within the CPA. The SGPM interactions can subsequently be used in thermodynamic Monte-Carlo simulations or mean field approximations to determine the ordering phe- nomena in binary alloys.
    [Show full text]
  • Ordering Phenomena of High-Spin/Low-Spin States In
    Ordering phenomena of high-spin/low-spin states in stepwise spin-crossover materials described by the ANNNI model Hiroshi Watanabe, Koichiro Tanaka, Nicolas Brefuel, Hervé Cailleau, Jean-François Létard, Sylvain Ravy, Pierre Fertey, Masamichi Nishino, Seiji Miyashita, Eric Collet To cite this version: Hiroshi Watanabe, Koichiro Tanaka, Nicolas Brefuel, Hervé Cailleau, Jean-François Létard, et al.. Ordering phenomena of high-spin/low-spin states in stepwise spin-crossover materials described by the ANNNI model. Physical Review B, American Physical Society, 2016, 93 (1), pp.014419. 10.1103/PhysRevB.93.014419. hal-01255817 HAL Id: hal-01255817 https://hal.archives-ouvertes.fr/hal-01255817 Submitted on 15 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICAL REVIEW B 93, 014419 (2016) Ordering phenomena of high-spin/low-spin states in stepwise spin-crossover materials described by the ANNNI model Hiroshi Watanabe,1,2 Koichiro Tanaka,3 Nicolas Brefuel,´ 4 Herve´ Cailleau,1 Jean-Franc¸ois Letard,´ 5 Sylvain Ravy,6,7 Pierre Fertey,6 Masamichi
    [Show full text]
  • Arxiv:1904.01486V1 [Cond-Mat.Str-El] 2 Apr 2019 Or in Their Derivatives
    Unveiling phase transitions with machine learning Askery Canabarro,1, 2 Felipe Fernandes Fanchini,3 André Luiz Malvezzi,3 Rodrigo Pereira,1, 4 and Rafael Chaves1, 5 1International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil 2Grupo de Física da Matéria Condensada, Núcleo de Ciências Exatas - NCEx, Campus Arapiraca, Universidade Federal de Alagoas, 57309-005 Arapiraca-AL, Brazil 3Faculdade de Ciências, Universidade Estadual Paulista, 17033-360 Bauru-SP, Brazil 4Departamento de Física Teórica e Experimental, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil 5School of Science and Technology, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil (Dated: April 3, 2019) The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singu- larities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning tech- niques. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neighbour interactions are introduced. All our results rely on few and low dimen- sional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.
    [Show full text]