Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method
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Quantum Phase Transitions in Collective Spin Models
Quantum Phase Transitions in Collective Spin Models. Applications to Adiabatic Quantum Computation Pedro Ribeiro To cite this version: Pedro Ribeiro. Quantum Phase Transitions in Collective Spin Models. Applications to Adiabatic Quantum Computation. Quantum Physics [quant-ph]. Université Pierre et Marie Curie - Paris VI, 2008. English. NNT : 2008PA066235. tel-00812554 HAL Id: tel-00812554 https://tel.archives-ouvertes.fr/tel-00812554 Submitted on 12 Apr 2013 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. i Auteur: Pedro RIBEIRO, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Universit´ePierre et Marie Curie Tour 24, Boˆıte 121, 4, Place Jussieu, 75252 Paris Cedex 05, France . 2008 ii Transitions de Phase Quantiques dans des Mod`eles de Spin Collectif. Applications au Calcul Adiabatique R´esum´e Partie I: Mod`eles de spin collectif On utilise le formalisme des ´etats coh´erents de spin pour ´etudier des mod`eles de spin collectif, qui ont plusieurs champs d’application en physique. Le mod`ele de Lipkin-Meshkov-Glick (LMG) a en particulier ´et´eanalys´e`ala limite thermodynamique. La m´ethode d´evelopp´ee au cours de ce travail peut ˆetre utilis´ee, en principe, pour des Hamiltoniens plus g´en´eraux, s’´ecrivant en fonction des g´en´erateurs de l’alg`ebre su(2). -
Quantum Many-Body States Defined Through Conformal Field Theory
Technische Universität München Max-Planck-Institut für Quantenoptik Quantum many-body states defined through conformal field theory Benedikt Thomas Herwerth Vollständiger Abdruck der von der Fakultät für Physik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Prof. Dr. Alexander Holleitner Prüfer der Dissertation: 1. Hon.-Prof. J. Ignacio Cirac, Ph.D. 2. Prof. Dr. Frank Pollmann Die Dissertation wurde am 01.08.2018 bei der Technischen Universität München eingereicht und durch die Fakultät für Physik am 05.10.2018 angenommen. Abstract In this thesis, we study quantum many-body systems in one (1D) and in two spatial dimen- sions (2D). We adopt the approach established by Moore and Read, where model states are constructed using conformal field theory (CFT), a scale-invariant quantum field theory. The central themes of this thesis are the definition of states through CFT, their characterization, and the understanding of their properties in terms of the underlying CFT. The first part of this thesis considers a CFT with an additional SU(2) symmetry. We define a 1 map from CFT states to those of spin- 2 systems on lattices. In 1D, the CFT vacuum is mapped to the ground state of a Heisenberg-like spin chain with long-range inverse-square interactions. We show that the excited states of this spin chain can be constructed from excitations of the CFT. Thus, we establish a correspondence between the spectrum of the CFT and that of the spin chain. In a next step, we study these states in 2D, where the CFT ground state corresponds to a fractional quantum Hall (FQH) lattice state. -
Image Segmentation Combining Markov Random Fields and Dirichlet Processes
ANR meeting Image segmentation combining Markov Random Fields and Dirichlet Processes Jessica SODJO IMS, Groupe Signal Image, Talence Encadrants : A. Giremus, J.-F. Giovannelli, F. Caron, N. Dobigeon Jessica SODJO ANR meeting 1 / 28 ANR meeting Plan 1 Introduction 2 Segmentation using DP models Mixed MRF / DP model Inference : Swendsen-Wang algorithm 3 Hierarchical segmentation with shared classes Principle HDP theory 4 Conclusion and perspective Jessica SODJO ANR meeting 2 / 28 ANR meeting Introduction Segmentation – partition of an image in K homogeneous regions called classes – label the pixels : pixel i $ zi 2 f1;:::; K g Bayesian approach – prior on the distribution of the pixels – all the pixels in a class have the same distribution characterized by a parameter vector Uk – Markov Random Fields (MRF) : exploit the similarity of pixels in the same neighbourhood Constraint : K must be fixed a priori Idea : use the BNP models to directly estimate K Jessica SODJO ANR meeting 3 / 28 ANR meeting Segmentation using DP models Plan 1 Introduction 2 Segmentation using DP models Mixed MRF / DP model Inference : Swendsen-Wang algorithm 3 Hierarchical segmentation with shared classes Principle HDP theory 4 Conclusion and perspective Jessica SODJO ANR meeting 4 / 28 ANR meeting Segmentation using DP models Notations – N is the number of pixels – Y is the observed image – Z = fz1;:::; zN g – Π = fA1;:::; AK g is a partition and m = fm1;:::; mK g with mk = jAk j A1 A2 m1 = 1 m2 = 5 A3 m3 = 6 mK = 4 AK FIGURE: Example of partition Jessica SODJO ANR -
Lecturenotes 4 MCMC I – Contents
Lecturenotes 4 MCMC I – Contents 1. Statistical Physics and Potts Models 2. Sampling and Re-weighting 3. Importance Sampling and Markov Chain Monte Carlo 4. The Metropolis Algorithm 5. The Heatbath Algorithm (Gibbs Sampler) 6. Start and Equilibration 7. Energy Checks 8. Specific Heat 1 Statistical Physics and Potts Model MC simulations of systems described by the Gibbs canonical ensemble aim at calculating estimators of physical observables at a temperature T . In the following we choose units so that β = 1/T and consider the calculation of the expectation value of an observable O. Mathematically all systems on a computer are discrete, because a finite word length has to be used. Hence, K X (k) Ob = Ob(β) = hOi = Z−1 O(k) e−β E (1) k=1 K X (k) where Z = Z(β) = e−β E (2) k=1 is the partition function. The index k = 1,...,K labels all configurations (or microstates) of the system, and E(k) is the (internal) energy of configuration k. To distinguish the configuration index from other indices, it is put in parenthesis. 2 We introduce generalized Potts models in an external magnetic field on d- dimensional hypercubic lattices with periodic boundary conditions. Without being overly complicated, these models are general enough to illustrate the essential features we are interested in. In addition, various subcases of these models are by themselves of physical interest. Generalizations of the algorithmic concepts to other models are straightforward, although technical complications may arise. We define the energy function of the system by (k) (k) (k) −β E = −β E0 + HM (3) where (k) X (k) (k) (k) (k) 2 d N E = −2 J (q , q ) δ(q , q ) + (4) 0 ij i j i j q hiji N 1 for qi = qj (k) X (k) with δ(qi, qj) = and M = 2 δ(1, qi ) . -
Mathematisches Forschungsinstitut Oberwolfach Scaling Limits in Models of Statistical Mechanics
Mathematisches Forschungsinstitut Oberwolfach Report No. 41/2018 DOI: 10.4171/OWR/2018/41 Scaling Limits in Models of Statistical Mechanics Organised by Dmitry Ioffe, Haifa Gady Kozma, Rehovot Fabio Toninelli, Lyon 9 September – 15 September 2018 Abstract. This conference (part of a long running series) aims to cover the interplay between probability and mathematical statistical mechanics. Specific topics addressed during the 22 talks include: Universality and critical phenomena, disordered models, Gaussian free field (GFF), random planar graphs and unimodular planar maps, reinforced random walks and non-linear σ-models, non-equilibrium dynamics. Less stress is given to topics which have running series of Oberwolfach conferences devoted to them specifically, such as random matrices or integrable models and KPZ universality class. There were 50 participants, including 9 postdocs and graduate students, working in diverse intertwining areas of probability, statistical mechanics and mathematical physics. Subject classification: MSC: 60,82; IMU: 10,13. Introduction by the Organisers This workshop was a sequel to a MFO conference, by the same organizers, which took place in 2015. More broadly, it is a sequel to MFO conferences in 2006, 2009 and 2012, organised by Ken Alexander, Marek Biskup, Remco van der Hofstad and Vladas Sidoravicius. The main focus of the conference remained on probabilistic and analytic methods of non-integrable statistical mechanics. With respect to the previous editions, greater emphasis was put on statistical mechanics models on groups and general graphs, as a lot has happened in this arena recently. The list of 50 participants reflects our attempts to maintain an optimal balance between diverse fields, leading experts and promising young researchers. -
Solid State Physics 2 Lecture 4: Magnetism in Charge Insulators
Physics 7450: Solid State Physics 2 Lecture 4: Magnetism in charge insulators Leo Radzihovsky (Dated: 19 February, 2015) Abstract In these lectures, we will study magnetism in insulators. After a warm up with paramagnetism of independent spins, we will discuss the spin exchange interactions in solids, arising from the combination of Coulomb repulsion and Pauli exclusion, and leads to the Heisenberg model of magnetism. Focussing on the simplest ferromagnetic and antiferromagnetic states, we will analyze thermodynamics and correlations of low-energy excitations around these states using Holstein- Primakoff and Schwinger bosons descriptions. We will use Jordan-Wigner transformation to solve a one-dimensional spin-1/2 chain. We will discuss coherent-spin states path-integral formulation of magnetism emphasizing, the role of Berry’s phase and will analyze phase transitions using Landau’s mean-field theory of FM and AFM phases. 1 I. INTRODUCTION A. Outline • Paramagnetism • Spin exchange vs dipolar interaction • Heisenberg model and crystalline anisotropies • Hostein-Primakoff and Schwinger bosons • Jordan-Wigner transformation and XXZ chain • Coherent-spin states and Berry phases • Mean-field and Landau theory of FM and AFM states B. Background In these notes we will explore some of aspects of magnetism in charge insulators. Mag- netism is a formation and response of magnetic moments to external magnetic field H and their interaction. In general there are two sources of magnetic moment and associated mag- netization density M. One is quite intuitive, due to orbital charge current j in the material 1 Z M = r × j, 2 r much like current wire loop produces magnetic field. -
Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets
nanomaterials Article Emergence of Nontrivial Spin Textures in Frustrated Van Der Waals Ferromagnets Aniekan Magnus Ukpong Theoretical and Computational Condensed Matter and Materials Physics Group, School of Chemistry and Physics, University of KwaZulu-Natal, Pietermaritzburg 3201, South Africa; [email protected]; Tel.: +27-33-260-5875 Abstract: In this work, first principles ground state calculations are combined with the dynamic evolution of a classical spin Hamiltonian to study the metamagnetic transitions associated with the field dependence of magnetic properties in frustrated van der Waals ferromagnets. Dynamically stabilized spin textures are obtained relative to the direction of spin quantization as stochastic solutions of the Landau–Lifshitz–Gilbert–Slonczewski equation under the flow of the spin current. By explicitly considering the spin signatures that arise from geometrical frustrations at interfaces, we may observe the emergence of a magnetic skyrmion spin texture and characterize the formation under competing internal fields. The analysis of coercivity and magnetic hysteresis reveals a dynamic switch from a soft to hard magnetic configuration when considering the spin Hall effect on the skyrmion. It is found that heavy metals in capped multilayer heterostructure stacks host field-tunable spiral skyrmions that could serve as unique channels for carrier transport. The results are discussed to show the possibility of using dynamically switchable magnetic bits to read and write data without the need for a spin transfer torque. These results offer insight to the spin transport signatures that Citation: Ukpong, A.M. Emergence dynamically arise from metamagnetic transitions in spintronic devices. of Nontrivial Spin Textures in Frustrated Van Der Waals Keywords: spin current; van der Waals ferromagnets; magnetic skyrmion; spin Hall effect Ferromagnets. -
The Information-Theoretic Structure of Classical Spin Systems
Santa Fe Institute Working Paper 15-10-042 arXiv:1510.08954 [cond-mat.stat-mech] Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems Vikram S. Vijayaraghavan,∗ Ryan G. James,† and James P. Crutchfield‡ Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616 (Dated: August 16, 2016) Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system’s observed emergent patterns. Recent developments in information theory, however, suggest quantifying collective organization in a system- and phenomenon-agnostic way: decompose the system’s thermodynamic entropy density into a localized entropy, that solely contained in the dynamics at a single location, and a bound entropy, that stored in space as domains, clusters, excitations, or other emergent structures. We compute this decomposition and related quantities explicitly for the nearest-neighbor Ising model on the 1D chain, the Bethe lattice with coordination number k = 3, and the 2D square lattice, illustrating its generality and the functional insights it gives near and away from phase transitions. In particular, we consider the roles that different spin motifs play (in cluster bulk, cluster edges, and the like) and how these affect the dependencies between spins. PACS numbers: 05.20.-y 89.75.Kd 05.45.-a 02.50.-r 89.70.+c Keywords: Ising spin model, thermodynamic entropy density, dual total correlation, entropy rate, elusive information, enigmatic information, predictable information rate, complex system I. INTRODUCTION statistical mechanics. Both Shaw [9] and Arnold [10] studied information in 1D spin-strips within the 2D Ising Collective behavior underlies a vast array of fascinating model. -
Arxiv:1511.03031V2
submitted to acta physica slovaca 1– 133 A BRIEF ACCOUNT OF THE ISING AND ISING-LIKE MODELS: MEAN-FIELD, EFFECTIVE-FIELD AND EXACT RESULTS Jozef Streckaˇ 1, Michal Jasˇcurˇ 2 Department of Theoretical Physics and Astrophysics, Faculty of Science, P. J. Saf´arikˇ University, Park Angelinum 9, 040 01 Koˇsice, Slovakia The present article provides a tutorial review on how to treat the Ising and Ising-like models within the mean-field, effective-field and exact methods. The mean-field approach is illus- trated on four particular examples of the lattice-statistical models: the spin-1/2 Ising model in a longitudinal field, the spin-1 Blume-Capel model in a longitudinal field, the mixed-spin Ising model in a longitudinal field and the spin-S Ising model in a transverse field. The mean- field solutions of the spin-1 Blume-Capel model and the mixed-spin Ising model demonstrate a change of continuous phase transitions to discontinuous ones at a tricritical point. A con- tinuous quantum phase transition of the spin-S Ising model driven by a transverse magnetic field is also explored within the mean-field method. The effective-field theory is elaborated within a single- and two-spin cluster approach in order to demonstrate an efficiency of this ap- proximate method, which affords superior approximate results with respect to the mean-field results. The long-standing problem of this method concerned with a self-consistent deter- mination of the free energy is also addressed in detail. More specifically, the effective-field theory is adapted for the spin-1/2 Ising model in a longitudinal field, the spin-S Blume-Capel model in a longitudinal field and the spin-1/2 Ising model in a transverse field. -
Random and Out-Of-Equilibrium Potts Models Christophe Chatelain
Random and Out-of-Equilibrium Potts models Christophe Chatelain To cite this version: Christophe Chatelain. Random and Out-of-Equilibrium Potts models. Statistical Mechanics [cond- mat.stat-mech]. Université de Lorraine, 2012. tel-00959733 HAL Id: tel-00959733 https://tel.archives-ouvertes.fr/tel-00959733 Submitted on 15 Mar 2014 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. Habilitation `aDiriger des Recherches Mod`eles de Potts d´esordonn´eset hors de l’´equilibre Christophe Chatelain Soutenance publique pr´evue le 17 d´ecembre 2012 Membres du jury : Rapporteurs : Werner Krauth Ecole´ Normale Sup´erieure, Paris Marco Picco Universit´ePierre et Marie Curie, Paris 6 Heiko Rieger Universit´ede Saarbr¨ucken, Allemagne Examinateurs : Dominique Mouhanna Universit´ePierre et Marie Curie, Paris 6 Wolfhard Janke Universit´ede Leipzig, Allemagne Bertrand Berche Universit´ede Lorraine Institut Jean Lamour Facult´edes Sciences - 54500 Vandœuvre-l`es-Nancy Table of contents 1. Random and Out-of-Equililibrium Potts models 4 1.1.Introduction................................. 4 1.2.RandomPottsmodels .......................... 6 1.2.1.ThepurePottsmodel ......................... 6 1.2.1.1. Fortuin-Kasteleyn representation . 7 1.2.1.2. From loop and vertex models to the Coulomb gas . -
The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B 879 [FS] (2014) 382–406 www.elsevier.com/locate/nuclphysb The staggered six-vertex model: Conformal invariance and corrections to scaling Holger Frahm a,∗, Alexander Seel b a Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany b Lehrstuhl für Theoretische Elektrotechnik und Photonik, Universität Siegen, Hölderlinstraße 3, 57068 Siegen, Germany Received 2 December 2013; received in revised form 16 December 2013; accepted 23 December 2013 Available online 31 December 2013 Abstract We study the emergence of non-compact degrees of freedom in the low energy effective theory for a class of Z2-staggered six-vertex models. In the finite size spectrum of the vertex model this shows up through the appearance of a continuum of critical exponents. To analyze this part of the spectrum we derive a set of coupled nonlinear integral equations from the Bethe ansatz solution of the vertex model which allow to compute the energies of the system for a range of anisotropies and of the staggering parameter. The critical theory is found to be independent of the staggering. Its spectrum and density of states coincide with the SL(2, R)/U(1) Euclidean black hole conformal field theory which has been identified previously in the continuum limit of the vertex model for a particular ‘self-dual’ choice of the staggering. We also study the asymptotic behavior of subleading corrections to the finite size scaling and discuss our findings in the context of the conformal field theory. © 2014 The Authors. Published by Elsevier B.V. -
Theory of Continuum Percolation I. General Formalism
Theory of continuum percolation I. General formalism Alon Drory Dipartimento di Fisica, Universit´a La Sapienza Piazzale Aldo Moro 2, Roma 00187, Italy Abstract The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A ba- sis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting s-state spins which are free to move in the continuum. In the s → 1 limit, the Potts magnetization, suscepti- bility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respec- tively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem. arXiv:cond-mat/9606195v1 26 Jun 1996 1 1 Introduction The theoretical basis of continuum percolation [1] changed drastically during the 1970’s. In their seminal 1970 paper, Scher and Zallen [2] considered continuum percolation as an extension of lattice models. Noting that the critical volume φc is approximately universal, i. e., essentially independent of the lattice structure, they suggested it might be carried over into continuum systems. Such a view of the continuum as the representation of what is lattice- independent sits well with the ideas of the renormalization group where the continuum often represents merely a scale at which the underlying lattice blurs and vanishes. Yet continuum percolation turned out to be much richer than suggested by this conception.