Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus

2000/09/30 by J. Salas, Jesús Salas · 4 citations
Mathematics · Physics and Astronomy · #Geometry #Ising model #Markov Chains and Monte Carlo Methods #Mathematical physics #Mathematics #Physics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Torus #cond-mat.stat-mech #hep-lat

paper · pdf · doi:10.1088/0305-4470/34/7/307

published as J.Phys.A34:1311-1331,2001 · 26 pages (LaTeX). Self-unpacking file containing the tex file and three macros (indent.sty, eqsection.sty, subeqnarray.sty). Added discussions on the results and new references. Version to be published in J. Phys. A

openalex publication_date 2001/02/09 · arxiv created 2001/02/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We analyse the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-½ Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L -3 to the energy and the corrections of order L -2 and L -3 to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L -1 occur, unmodified by logarithms (except of course for the leading log L term in the specific heat); and the energy expansion contains only odd powers of L -1 . In the specific-heat expansion any power of L -1 can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.

Citations

• Geometry, thermodynamics, and finite-size corrections in the critical Potts model
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• Ising model on nonorientable surfaces: Exact solution for the Möbius strip and the Klein bottle
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

Cited by

• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Small-System Group: Thermodynamics as a Complete Self-Similarity Limit
• Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions
• Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices