Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

Article

关键词: HIGH-TEMPERATURE SERIES;    RENORMALIZED COUPLING-CONSTANTS;    CRITICAL-POINT SCATTERING;    LINKED-CLUSTER-EXPANSION;    MONTE-CARLO COMPUTATION;    VECTOR SPIN MODELS;    CRITICAL EXPONENTS;    3 DIMENSIONS;    DIFFERENTIAL APPROXIMANTS;    CRITICAL BEHAVIOUR;   

DOI  :  10.1103/PhysRevB.83.054433

来源: SCIE

【 摘 要 】

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s = 1,3/ 2,... and for the lattice Euclidean scalar-field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices. Our bivariate high-temperature expansions, which extend through 24th order, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely, all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.

【 授权许可】

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