Curie–Weiss magnet—a simple model of phase transition

@article{Kochmaski2013CurieWeissMS,
  title={Curie–Weiss magnet—a simple model of phase transition},
  author={M. S. Kochmański and Tadeusz Paszkiewicz and S. Wołski},
  journal={European Journal of Physics},
  year={2013},
  volume={34},
  pages={1555 - 1573}
}
The Curie–Weiss model is an exactly solvable model of ferromagnetism that allows one to study thermodynamic functions in detail, in particular their properties near the critical temperature. In this model every magnetic moment interacts with every other magnetic moment. Because of its simplicity and the correctness of at least some of its predictions, the Curie–Weiss model occupies an important place in the statistical mechanics literature and its application to information theory. It is… 

Spontaneous magnetization of ferromagnet in mean-field Heisenberg model

The Heisenberg ferromagnet model has been studied theoretically using the Weiss mean-field theory and Green’s function technique. The equations for the Curie temperature, magnetization, and magnetic

On the Landau theory of phase transitions: a hierarchical dynamic model

  • John Y. Fu
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2013
TLDR
The Landau theory of phase transitions has been re-examined under the framework of a modified mean field theory in ferroelectrics and it turns out that it is the behavior of the nematic phase on approaching the critical point that makes the Landau Theory deviate from experimental observations.

Quantum Curie-Weiss Magnet Induced by Violation of Cluster Property

  • T. Munehisa
  • Physics
    World Journal of Condensed Matter Physics
  • 2020
There are some concepts that are accepted in our daily life but are not trivial in physics. One of them is the cluster property that means there exist no relations between two events which are

Order Parameter in Short-Range and Long-Range Ising Finite Feromagnetic Models

The approach to determination of the order parameter in the finite 1D Ising model was proposed. For such systems a root mean square magnetization and an average size of the maximal ground state

Estimation of Local Microcanonical Averages in Two Lattice Mean-Field Models Using Coupling Techniques

We consider an application of probabilistic coupling techniques which provides explicit estimates for comparison of local expectation values between label permutation invariant states, for instance,

Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevance

The recent progress in the theory of generalised Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical

Analytic solutions of the modified Langevin equation in a mean-field model

Approximate analytical solutions of the modified Langevin equation are obtained. These solutions are relatively simple and enough accurate. They are illustrated by considering a mean-field model of a

Partition Function and Density of States in Models of a Finite Number of Ising Spins with Direct Exchange between the Minimum and Maximum Number of Nearest Neighbors

The results of studies of 1D Ising models and Curie-Weiss models partition functions structure are presented in this work. Exact calculation of the partition function using the authors combinatorial

Equivalence of ensembles in Curie-Weiss models using coupling techniques

We consider equivalence of ensembles for two mean field models: the discrete, standard Curie-Weiss model and its continuum version, also called the mean-field spherical model. These systems have two

References

SHOWING 1-10 OF 20 REFERENCES

Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions

By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase

The Theory of Critical Phenomena: An Introduction to the Renormalization Group

Here is a much-needed basic text that covers a vital area in physics for beginning graduate students. The successful calculation of critical exponents for continuous phase transitions is one of the

A Short Course on Mean Field Spin Glasses

We give a brief introduction to the theory of mean field models of spin glasses. This includes a concise presentation of the Random Energy model and the Generalized Random Energy model and the

Statistical physics of spin glasses and information processing : an introduction

1. Mean-field theory of phase transitions 2. Mean-field theory of spin glasses 3. Replica symmetry breaking 4. Gauge theory of spin glasses 5. Error-correcting codes 6. Image restoration 7.

Modern Theory of Critical Phenomena

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental

Statistical and Thermal Physics with Computer Applications

This article reviews Statistical and Thermal Physics with Computer Applications by Harvey Gould, Jan Tobochnik . 511 pp., , Princeton, NJ, 2010. $75.00(cloth) ISBN 978-0-691-13744-5.

Statistical Physics and Information Theory

  • N. Merhav
  • Physics
    Found. Trends Commun. Inf. Theory
  • 2010
TLDR
This chapter discusses the Random Energy Model and Random Coding, as well as analysis tools and Asymptotic Methods, and the physical interpretation of information measures.

The Theory of critical phenomena

Here is a much-needed basic text that covers a vital area in physics for beginning graduate students.

Statistical Mechanics (Hoboken, NJ: Wiley

  • 1987

Handbook of Mathematics 4th edn (Berlin: Springer

  • 2004