2010/12/22 by P. Butera, M. Pernici · 17 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Euclidean geometry #Geometry #Ising model #Markov Chains and Monte Carlo Methods #Mathematical physics #Mathematics #Phase transition #Physics #Potts model #Pure mathematics #Quartic function #Renormalization group #Scaling #Square-lattice Ising model #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1103/physrevb.83.054433
published in Physical Review B 83(5) (American Physical Society) · 22 pages, 10 figures
arxiv created 2010/12/22 · openalex publication_date 2011/02/25 · arxiv updated 2011/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.