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

Abstract

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 K^24, 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.

arXiv comment22 pages, 10 figures

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Cited by in corpus (10)

• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 <= d <= 7
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• Higher order expansions for the entropy of a dimer or a monomer-dimer system on d-dimensional lattices
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Universal effective couplings of the three-dimensional $n$-vector model and field theory