Journal ArticleDOI
Effect of Change of Spin on the Critical Properties of the Ising and Heisenberg Models
C. Domb,M. F. Sykes +1 more
TLDR
In this article, high-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$ for fcc lattice for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence.Abstract:
High-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$. The fcc lattice is used for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence. It is suggested that the magnetic susceptibility above the Curie temperature is of the form $A{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{4}{3}}$ for the Heisenberg model for all $s$, instead of ${A}^{\ensuremath{'}}{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{5}{4}}$ for the Ising model. Critical estimates of energy and entropy show that the magnitude of the "tail" of the specific heat anomaly is insensitive to the value of $s$, and is about 2.5 times larger for the Heisenberg than for the Ising model. The sharpness of the anomaly at the Curie point increases as $s$ increases, and on passing from the Heisenberg to the Ising model. A brief reference is made to experimental results.read more
Citations
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Journal ArticleDOI
The theory of equilibrium critical phenomena
TL;DR: The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations as mentioned in this paper.
Journal ArticleDOI
Static Phenomena Near Critical Points: Theory and Experiment
Leo P. Kadanoff,Wolfgang Götze,David Hamblen,Robert Hecht,E. A. S. Lewis,V. V. Palciauskas,Martin Rayl,Jack Swift,D. E. Aspnes,Joseph W. Kane +9 more
TL;DR: In this paper, the authors compared theory and experiment for behavior very near critical points, and suggested that scaling laws provide a promising approach to understand phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.
Journal ArticleDOI
Detailed Magnetic Behavior of Nickel Near its Curie Point
J. S. Kouvel,Michael E. Fisher +1 more
TL;DR: In this article, the authors derived the temperature dependence of the initial susceptibility of nickel above the Curie point and the field dependence of its magnetization at the same point from the data of Weiss and Forrer and found that the results were at variance with the simple molecular field model.
Journal ArticleDOI
Renormalization group theory: Its basis and formulation in statistical physics
TL;DR: The nature and origins of renormalization group ideas in statistical physics and condensed matter theory are recounted informally, emphasizing those features of prime importance in these areas of science in contradistinction to quantum field theory, in particular: critical exponents and scaling, relevance, irrelevance and marginality, universality, and Wilson's crucial concept of flows and fixed points as mentioned in this paper.
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