DOCSLIB.ORG

Curie Point of Ferromagnets

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Curie Point of Ferromagnets Eur. J. Phys. 18 (1997) 448–452. Printed in the UK PII: S0143-0807(97)84690-9 Curie point of ferromagnets Yaakov Kraftmakher Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel Received 4 June 1997, in final form 18 August 1997 Abstract. A student experiment is described concerning Zusammenfassung. Ein Studentenexperiment in Beziehung properties of ferromagnets near the Curie point. Gadolinium der Eigenschaften eines Ferromagnetikums nahe des provides a good opportunity to determine the magnetic Curie-Punktes ist beschrieben. Gadolinium bietet eine gute susceptibility above the transition point and to evaluate the Gelegenheit, die magnetische Suszeptibilitat¨ uber¨ der critical exponent of the susceptibility. The temperature Ubergangstemperatur¨ auszuwerten und den kritischen dependence of the electrical resistance of nickel at enhanced Exponent der Suszeptibilitat¨ berechnen. Die frequencies shows the influence of the magnetic properties of Temperaturabhangigkeit¨ des elektrischen Widerstandes des the sample on the skin depth. From the measurements, the Nickels in hoheren¨ Frequenzen demonstriert den Einfluß der phase transition is clearly seen and the temperature magnetischen Eigenschaften der Probe auf die Skinschicht. dependence of the magnetic permeability below the Curie Von den Messungen, der Phasenubergang¨ ist klar und die point is available. Data on the resistance at an enhanced Temperaturabhandigkeit¨ der magnetischen Permeabilitat¨ unter frequency reveal the phase transition in a nickel-based alloy. der Curie-Temperatur kann berechnet werden. Die Daten des These items may be added to related student experiments Widerstandes in hoheren¨ Frequenzen enthullen¨ den described previously. Phasenubergang¨ in einer Nickellegierung. Vorher beschriebene Studentenexperimente konnen¨ mit obigen Punkten erganzt¨ werden. 1. Introduction One of the most important objectives of the theory and experiment is to determine the critical exponents. At temperatures above the Curie temperature, TC,a The mean-field theory predicted values of the critical ferromagnet loses its intrinsic magnetization. The exponents as follows: α 0,β 0.5,γ 1. transition from the magnetic to the nonmagnetic state However, observed dependences= appeared= to be= quite is a second-order phase transition. Many properties of different. The modern theory of critical phenomena a ferromagnet manifest singularities near the transition can be found elsewhere (Ma 1976, Patashinskii and point, usually with a power-like dependence (e.g. Fisher Pokrovskii 1979, Stanley 1983, Domb 1996). In 1965, 1967, Heller 1967, Kadanoff et al 1967). The 1982, Kenneth G Wilson was awarded the Nobel Prize exponent in such a dependence is referred to as the in Physics ‘for his theory for critical phenomena in critical exponent or critical index. For instance, the connection with phase transitions’ (see Wilson 1993). temperature dependence of the specific heat, C, follows The theory is very complicated but Maris and Kadanoff the equation (1978) have shown how Wilson’s theory could be α incorporated into an undergraduate course of statistical C A B T T − (1) = + | − C| physics. At present, the accepted theoretical values where A and B are constants, generally different below are as follows: α 0.115 0.009,β 0.3645 and above the Curie point, and α is termed the critical 0.0025,γ 1.386 =−0.004 (Domb± 1996).= Generally,± exponent of the specific heat. experimentally= determined± critical exponents are, to Below the transition point, the spontaneous magneti- within experimental errors, in agreement with these zation of a ferromagnet, M, obeys the relation theoretical values. The theory also predicts some relations between the critical exponents, e.g. a relation M A(T T)β (2) = C − fitting the above critical exponents: where β denotes the critical exponent of the spontaneous α 2β γ 2. (4) magnetization. + + ≥ Close to the Curie point, the magnetic susceptibility, Both sets of critical exponents given above fulfil χ, is given by this relation even as an equality. The parameters γ and critical exponents describing the phase transition χ A T T − (3) = | − C| in a ferromagnet are similar to those for the critical where γ is the critical exponent of the susceptibility. point of the liquid–vapour coexistence curve. The 0143-0807/97/060448+05$19.50 c 1997 IOP Publishing Ltd & The European Physical Society 448 Curie point of ferromagnets 449 magnetization is analogous to the difference between the D C density of the fluid and the critical density, whereas the source magnetic susceptibility is analogous to the isothermal compressibility of the fluid. Several student experiments related to the Curie point L F Keithley oscillator thermistor have already been described. Two of these employ sample 199 DMM the mutual inductance technique for determining the Curie point of ferromagnets (Edgar and Quilty 1993, selective Scanner Fisher and Franz 1995). Other experiments include heater amplifier measurements of the electrical resistivity of nickel (Kamal et al 1983, Fox et al 1986, Sullivan et al 1987) differential and observations of changes in the resonant frequency transformer of an LC circuit when the sample placed inside the inductor undergoes the transition (Fox et al 1986). Figure 1. Set-up to measure the magnetic susceptibility Two items described below may be added to the of gadolinium. student experiments reported earlier, namely: (i) the magnetic susceptibility of a ferromagnet above the Curie AC current creates a magnetic flux in the magnetic core. point; (ii) the influence of the magnetic properties of Two secondary windings (n 400) are connected in a ferromagnet on the skin depth when an AC current 2 opposition; thus without a sample= no voltage appears passes through the sample. at the transformer’s output. A small additional coil In the first part, the magnetic susceptibility of connected in series with the secondary windings is used gadolinium is measured above the Curie point. When to finely balance the transformer. This coil is placed approaching the Curie point, the magnetic susceptibility near the core to obtain the necessary compensation depends on the quality of the sample and on the voltage. With a magnetic sample in the gap of the approach to the transition point. In magnetic core, the magnetic flux through this part of the core measurements, this approach was limited by the value 4 3 increases. This causes an increase in the voltage induced of T TC /TC in the range 10− –10− . With such a proximity,| − | the magnetic susceptibility above the in the corresponding secondary winding. To avoid the Curie point may be much smaller than that in the influence of eddy currents in the sample, the operating ferromagnetic phase (e.g. Heller 1967, Herzum et al frequency is reduced to 30 Hz. 1974). Gadolinium is rather an exception that possesses A spherical gadolinium sample (99.9%), 5 mm in a high magnetic susceptibility above the Curie point. diameter, is placed into a small glass container filled It allows one to perform the measurements over a with oil to reduce temperature gradients and to prevent wide temperature interval in the nonmagnetic phase oxidation of the sample. A small thermistor (Fenwal and to evaluate the critical exponent of the magnetic Electronics, model UUA 35J3, 5000 at 25 ◦C) is susceptibility. attached to the sample. Its resistance, R, relates to the absolute temperature as T 3895/ ln(R/0.0106).A In the second part, the temperature dependence of = the electrical resistance of nickel is measured using a bifilar electrical heater is also inserted in the oil. The DC current and an AC current of enhanced frequency. heater and the thermistor contain no magnetic parts. The transition to the nonmagnetic state becomes evident The internal magnetic field in the sample, Hi, should owing to a change in the skin depth. Moreover, the be calculated taking into account the demagnetizing temperature dependence of the magnetic permeability factor, α. Thus, the magnetization is M = of the sample can be evaluated from the ratio of the χHi χ(He αM), where He is the external = − electrical impedance of the sample to its DC resistance. field. Hence, M He/(α 1/χ). The output = + Similar measurements reveal the phase transition in a voltage of the differential transformer is proportional nickel-based alloy. to the magnetization of the sample: V KM = = KHe/(α 1/χ). Below the Curie point, 1/χ α. This assumption+ allows one to determine the external 2. Magnetic susceptibility of gadolinium magnetic field: He αV0/K, where V0 is the output voltage below T .= For a sphere, α 1 (SI units). C = 3 The aim of this experiment is to determine the magnetic Hence, χ 3V /(V0 V). The absolute value of the = − susceptibility of gadolinium above the Curie point. magnetic susceptibility is thus available (Heller 1967). Gadolinium provides a very convenient temperature of The output voltage of the differential transformer is the phase transition and a relatively large interval where fed to an amplifier, PAR model 124A. The amplifier the magnetic susceptibility can be measured. operates in the selective mode and is tuned to the signal For the measurements, an E-shaped transformer is frequency. The amplified voltage is monitored by an employed. The core and the coils have been purchased oscilloscope. For initial balancing of the transformer, from PASCO, catalogue numbers SF-8615, SF-8610 it is more convenient to observe the Lissajous pattern and SF-8611. The primary winding (n1 800) is on the oscilloscope’s screen. For this purpose, the connected to a low-frequency oscillator (figure= 1). The voltage drop across a resistor connected in series with 450 Y Kraftmakher 100 6 290.5 K 4 χ 291 K 290 K 50 ln 2 0 Magnetic susceptibility Magnetic 0 290 295 300 305 K Figure 2. Temperature dependence of the magnetic -2024 susceptibility of gadolinium. − ln (T Tc) Figure 3. Plot of ln χ versus ln(T TC). Determination the primary winding of the transformer is fed to the of γ includes the choice of the transition− temperature.
Load more

Recommended publications
  • International Centre for Theoretical Physics
    REFi IC/90/116 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS FIXED SCALE TRANSFORMATION FOR ISING AND POTTS CLUSTERS A. Erzan and L. Pietronero INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1990 MIRAMARE- TRIESTE IC/90/116 International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS FIXED SCALE TRANSFORMATION FOR ISING AND POTTS CLUSTERS A. Erzan International Centre for Theoretical Physics, Trieste, Italy and L. Pietronero Dipartimento di Fisica, Universita di Roma, Piazzale Aldo Moro, 00185 Roma, Italy. ABSTRACT The fractal dimension of Ising and Potts clusters are determined via the Fixed Scale Trans- formation approach, which exploits both the self-similarity and the dynamical invariance of these systems at criticality. The results are easily extended to droplets. A discussion of inter-relations be- tween the present approach and renormalization group methods as well as Glauber—type dynamics is provided. MIRAMARE - TRIESTE May 1990 To be submitted for publication. T 1. INTRODUCTION The Fixed Scale Transformation, a novel technique introduced 1)i2) for computing the fractal dimension of Laplacian growth clusters, is applied here to the equilibrium problem of Ising clusters at criticality, in two dimensions. The method yields veiy good quantitative agreement with the known exact results. The same method has also recendy been applied to the problem of percolation clusters 3* and to invasion percolation 4), also with very good results. The fractal dimension D of the Ising clusters, i.e., the connected clusters of sites with identical spins, has been a controversial issue for a long time ^ (see extensive references in Refs.5 and 6).
    [Show full text]
  • Phase Transitions and Critical Phenomena: an Essay in Natural Philosophy (Thales to Onsager)
    Phase Transitions and Critical Phenomena: An Essay in Natural Philosophy (Thales to Onsager) Prof. David A. Edwards Department of Mathematics University of Georgia Athens, Georgia 30602 http://www.math.uga.edu/~davide/ http://davidaedwards.tumblr.com/ [email protected] §1. Introduction. In this essay we will present a detailed analysis of the concepts and mathematics that underlie statistical mechanics. For a similar discussion of classical and quantum mechanics the reader is referred to [E-1] and [E-4]. For a similar discussion of quantum field theory the reader is referred to [E-2]. For a discussion of quantum geometrodynamics the reader is referred to [E- 3] Scientific theories go through many stages in their development, some eventually reaching the stage at which one might say that "the only work left to be done is the computing of the next decimal." We shall call such theories climax theories in analogy with the notion of a climax forest (other analogies are also appropriate). A climax theory has two parts: one theoretical, which has become part of pure mathematics; and the other empirical, which somehow relates the mathematics to experience. The earliest example of a climax theory is Euclidean geometry. That such a development of geometry is even possible is not obvious. One can easily imagine an Egyptian geometer explaining to a Babylonian number theorist why geometry could never become a precise science like number theory because pyramids and other such bodies are intrinsically irregular and fuzzy (similar discussions occur often today between biologists and physicists). Archimedes' fundamental work showing that the four fundamental constants related to circles and spheres (C =αr, A = βr2 , S = ϒr 2, V= δr3 ) are all simply related (1/2α=β = 1/4ϒ= 3/4δ= π), together with his estimate that 3+10/71< π < 3+1/7 will serve for us as the paradigm of what science should be all about.
    [Show full text]
  • Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point
    entropy Article Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point Juan Carlos Obeso-Jureidini , Daniela Olascoaga and Victor Romero-Rochín * Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México 01000, Mexico; [email protected] (J.C.O.-J.); [email protected] (D.O.) * Correspondence: romero@fisica.unam.mx; Tel.: +52-55-5622-5096 Abstract: With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so. Keywords: liquid–vapor critical point; scaling hypothesis; critical exponents Citation: Obeso-Jureidini, J.C.; 1. Introduction Olascoaga, D.; Romero-Rochín, V. The full thermodynamic description of critical phenomena in the liquid–vapor phase Thermodynamic Derivation of transition of pure substances has remained as a theoretical challenge for a long time [1].
    [Show full text]
  • Classifying Potts Critical Lines
    Classifying Potts critical lines Gesualdo Delfino1,2 and Elena Tartaglia1,2 1SISSA – Via Bonomea 265, 34136 Trieste, Italy 2INFN sezione di Trieste Abstract We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points invariant under the permutational symmetry Sq in two dimensions, and show how one of these scattering solutions describes the ferromagnetic and square lattice antiferromagnetic critical lines of the q-state Potts model. Other solutions we determine should correspond to new critical lines. In particular, we obtain that a Sq-invariant fixed point can be found up to the maximal value q = (7+ √17)/2. This is larger than the usually assumed maximal value 4 and leaves room for a second order antiferromagnetic transition at q = 5. arXiv:1707.00998v2 [cond-mat.stat-mech] 16 Oct 2017 1 Introduction Symmetry plays a prominent role within the theory of critical phenomena. The circumstance is usually illustrated referring to ferromagnetism, for which systems with different microscopic real- izations but sharing invariance under transformations of the same group G of internal symmetry fall within the same universality class of critical behavior. In the language of the renormalization group (see e.g. [1]) this amounts to say that the critical behavior of these ferromagnets is ruled by the same G-invariant fixed point. In general, however, there are several G-invariant fixed points of the renormalization group in a given dimensionality. Even staying within ferromag- netism, a system with several tunable parameters may exhibit multicriticality corresponding to fixed points with the same symmetry but different field content.
    [Show full text]
  • Self-Organization, Critical Phenomena, Entropy Decrease in Isolated Systems and Its Tests
    International Journal of Modern Theoretical Physics, 2019, 8(1): 17-32 International Journal of Modern Theoretical Physics ISSN: 2169-7426 Journal homepage:www.ModernScientificPress.com/Journals/ijmtp.aspx Florida, USA Article Self-Organization, Critical Phenomena, Entropy Decrease in Isolated Systems and Its Tests Yi-Fang Chang Department of Physics, Yunnan University, Kunming, 650091, China Email: [email protected] Article history: Received 15 January 2019, Revised 1 May 2019, Accepted 1 May 2019, Published 6 May 2019. Abstract: We proposed possible entropy decrease due to fluctuation magnification and internal interactions in isolated systems, and these systems are only approximation. This possibility exists in transformations of internal energy, complex systems, and some new systems with lower entropy, nonlinear interactions, etc. Self-organization and self- assembly must be entropy decrease. Generally, much structures of Nature all are various self-assembly and self-organizations. We research some possible tests and predictions on entropy decrease in isolated systems. They include various self-organizations and self- assembly, some critical phenomena, physical surfaces and films, chemical reactions and catalysts, various biological membranes and enzymes, and new synthetic life, etc. They exist possibly in some microscopic regions, nonlinear phenomena, many evolutional processes and complex systems, etc. As long as we break through the bondage of the second law of thermodynamics, the rich and complex world is full of examples of entropy decrease. Keywords: entropy decrease, self-assembly, self-organizations, complex system, critical phenomena, nonlinearity, test. DOI ·10.13140/RG.2.2.36755.53282 1. Introduction Copyright © 2019 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo.
    [Show full text]
  • The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems Kyrill A
    Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems Kyrill A. Bugaev Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Abstract. We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model, which is successfully used to describe the phase transition between hadron gas and quark gluon plasma, and the Hills and Dales Model of surface partition. A complete analysis of the isobaric partition singularities of these models is done for finite volumes. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to study the phase transitions in finite systems rigorously. The strategic directions of future research opened by these exact results are also discussed. Keywords: Laplace-Fourier transform, statistical multifragmentation model, gas of bags model, phase transitions in finite systems PACS: 25.70. Pq, 21.65.+f, 24.10. Pa There is always sufficient amount of facts. Imagination is what we lack. D. I. Blokhintsev I. THEORETICAL DESCRIPTION OF PHASE TRANSITIONS IN FINITE SYSTEMS A rigorous theory of critical phenomena in finite systems was not built up to now. However, the experimental studies of phase transitions (PTs) in some systems demand the formulation of such a theory.
    [Show full text]
  • Boundary Conformal Field Theory at the Extraordinary Transition
    Prepared for submission to JHEP Boundary conformal field theory at the extraordinary transition: The layer susceptibility to O(") M. A. Shpot Institute for Condensed Matter Physics, 79011 Lviv, Ukraine E-mail: [email protected] Abstract: We present an analytic calculation of the layer (parallel) susceptibility at the extraordinary transition in a semi-infinite system with a flat boundary. Using the method of integral transforms put forward by McAvity and Osborn [Nucl. Phys. B 455(1995) 522] in the boundary CFT, we derive the coordinate-space representation of the mean-field propagator at the transition point. The simple algebraic structure of this function provides a practical possibility of higher-order calculations. Thus we calculate the explicit expression for the layer susceptibility at the extraordinary transition in the one-loop approximation. Our result is correct up to order O(") of the " = 4 − d expansion and holds for arbitrary width of the layer and its position in the half-space. We discuss the general structure of our result and consider the limiting cases related to the boundary operator expansion and (bulk) operator product expansion. We compare our findings with previously known results and less complicated formulas in the case of the ordinary transition. We believe that analytic results for layer susceptibilities could be a good starting point for efficient calculations of two-point correlation functions. This possibility would be of great importance given the recent breakthrough in bulk and boundary conformal field theories
    [Show full text]
  • Lectures on Conformal Field Theory Arxiv:1511.04074V2 [Hep-Th] 19
    Prepared for submission to JHEP Lectures on Conformal Field Theory Joshua D. Quallsa aDepartment of Physics, National Taiwan University, Taipei, Taiwan E-mail: [email protected] Abstract: These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions working toward current research topics in conformal field theory. We assume the reader to be familiar with quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help. These notes include over 80 homework problems and over 45 longer exercises for students. arXiv:1511.04074v2 [hep-th] 19 May 2016 Contents 1 Lecture 1: Introduction and Motivation2 1.1 Introduction and outline2 1.2 Conformal invariance: What?5 1.3 Examples of classical conformal invariance7 1.4 Conformal invariance: Why?8 1.4.1 CFTs in critical phenomena8 1.4.2 Renormalization group 12 1.5 A preview for future courses 16 1.6 Conformal quantum mechanics 17 2 Lecture 2: CFT in d ≥ 3 22 2.1 Conformal transformations for d ≥ 3 22 2.2 Infinitesimal conformal transformations for d ≥ 3 24 2.3 Special conformal transformations and conformal algebra 26 2.4 Conformal group 28 2.5 Representations of the conformal group 29 2.6 Constraints of Conformal
    [Show full text]
  • Monte Carlo Study of the Ordering in a Strongly Frustrated Liquid Crystal S
    Monte Carlo study of the ordering in a strongly frustrated liquid crystal S. George 1,2 , C. Bentham 1, X. Zeng 3, G. Ungar 3,4 and GA Gehring 1 1Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK 2 CERN, Route de Meyrin 385, 1217 Meyrin, Switzerland 3 Department of Materials Science and Engineering, University of Sheffield, Sheffield, S1 3JD 4 Department of Physics, Zhejiang Sci-Tech University, 310018 Hangzhou, China 64.60.-i 75.40.Mg Abstract We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shape liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one containing fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexagons are occupied by either all silicon or all fluorine chains. There are two phase transitions. If only pairwise interactions are included it is found that there is a novel fluctuating phase between the disordered phase and the fully ordered ground state. This did not agree with the experiments where an intermediate phase was seen that had long range order on one of the three sublattices. Agreement was found when the calculations were modified to include attractive three body interactions between the silicon chains.
    [Show full text]
  • Critical Phenomena and the Quantum Critical Point of Ferromagnetic Zr1Xnbxzn2
    PHYSICAL REVIEW LETTERS week ending PRL 96, 116404 (2006) 24 MARCH 2006 Critical Phenomena and the Quantum Critical Point of Ferromagnetic Zr1ÿxNbxZn2 D. A. Sokolov,1 M. C. Aronson,1 W. Gannon,1 and Z. Fisk2,* 1University of Michigan, Ann Arbor, Michigan 48109-1120, USA 2Florida State University, Tallahassee, Florida 32310-3706, USA (Received 6 December 2005; published 24 March 2006) We present a study of the magnetic properties of Zr1ÿxNbxZn2, using an Arrott plot analysis of the magnetization. The Curie temperature TC is suppressed to zero temperature for Nb concentration xC 0:083 0:002, while the spontaneous moment vanishes linearly with TC as predicted by the Stoner theory. The initial susceptibility displays critical behavior for x xC, with a critical exponent which smoothly crosses over from the mean field to the quantum critical value. For high temperatures and x xC, and for ÿ1 ÿ1 4=3 ÿ1 low temperatures and x xC we find that 0 aT , where 0 vanishes as x ! xC. The resulting magnetic phase diagram shows that the quantum critical behavior extends over the widest range of temperatures for x xC, and demonstrates how a finite transition temperature ferromagnet is trans- formed into a paramagnet, via a quantum critical point. DOI: 10.1103/PhysRevLett.96.116404 PACS numbers: 71.10.Hf, 75.10.Lp, 75.40.Cx Zero temperature phase transitions and their attendant heat capacity is maximized [24–28] while the electrical 1 quantum critical fluctuations have emerged as dominant resistivity evolves from / T for ÿ ÿC to the Fermi 2 features in the phase diagrams of different types of strongly liquid / T for ÿ > ÿC [19,29–31].
    [Show full text]
  • Equilibrium Critical Phenomena in Fluids and Mixtures
    : wil Phenomena I Fluids and Mixtures: 'w'^m^ Bibliography \ I i "Word Descriptors National of ac \oo cop 1^ UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director Equilibrium Critical Phenomena In Fluids and Mixtures: A Comprehensive Bibliography With Key-Word Descriptors Stella Michaels, Melville S. Green, and Sigurd Y. Larsen Institute for Basic Standards National Bureau of Standards Washington, D. C. 20234 4. S . National Bureau of Standards, Special Publication 327 Nat. Bur. Stand. (U.S.), Spec. Publ. 327, 235 pages (June 1970) CODEN: XNBSA Issued June 1970 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C 13.10:327), Price $4.00. NATtONAL BUREAU OF STAHOAROS AUG 3 1970 1^8106 Contents 1. Introduction i±i^^ ^ 2. Bibliography 1 3. Bibliographic References 182 4. Abbreviations 183 5. Author Index 191 6. Subject Index 207 Library of Congress Catalog Card Number 7O-6O632O ii Equilibrium Critical Phenomena in Fluids and Mixtures: A Comprehensive Bibliography with Key-Word Descriptors Stella Michaels*, Melville S. Green*, and Sigurd Y. Larsen* This bibliography of 1088 citations comprehensively covers relevant research conducted throughout the world between January 1, 1950 through December 31, 1967. Each entry is charac- terized by specific key word descriptors, of which there are approximately 1500, and is indexed both by subject and by author. In the case of foreign language publications, effort was made to find translations which are also cited. Key words: Binary liquid mixtures; critical opalescence; critical phenomena; critical point; critical region; equilibrium critical phenomena; gases; liquid-vapor systems; liquids; phase transitions; ternairy liquid mixtures; thermodynamics 1.
    [Show full text]
  • Nuclear Enthalpies
    Warszawa 2016 Non-extensive critical effects in the nuclear mean field J. Rozynek, Warsaw Nonextensive NJ-L model of QCD matter revisited Eur.Phys. J. A. (2016) with G. Wilk Nonextensive distributions for a relativistic Fermi gas Eur. Phys. J. A. (2015) Content: - Motivation - Example: NJL model of QCD Nonextensive NJL model: q_NJL - Results - Summary Motivation ● The critical phenomena in strongly interaction matter are generally investigated using the mean-field model and are characterized by well defined critical exponents. ● However, such models provide only average properties of the corresponding order parameters and neglect altogether their possible fluctuations. Also the possible long range effect and correlations are neglected in the mean field approach. ● One of the possible phenomenological ways to account for such effects is to use the nonextensive approach. ● Here we investigate the critical behavior in the nonextensive version of the Nambu Jona-Lasinio model (NJL). It allows to account for such effects in a phenomenological way by means of a single parameter q, the nonextensivity parameter. ● In particular, we show how the nonextensive statistics influences the region of the critical temperature and chemical potential in the NJL mean field approach. Motivation ● The critical phenomena in strongly interaction matter are generally investigated using the mean-field model and are characterized by well defined critical exponents. ● However, such models provide only average properties of the corresponding order parameters and neglect altogether their possible fluctuations. Also the possible long range effect and correlations are neglected in the mean field approach. ● One of the possible phenomenological ways to account for such effects is to use the nonextensive approach.
    [Show full text]