Logarithmic corrections to the Ising model free energy on lattices with conical singularities

Abstract

The free energy of a two-dimensional system at criticality has in general an universal part proportional the logarithm of the system size. This term was shown by Cardy and Peschel to be related to the curvature of the system, with smooth metrics and singular points contributing in distinct ways. In this paper we present a numerical study of the effect, for the Ising model on lattices with various topologies from the sphere to genus two surfaces. The nature of this term for specific lattice models is an open problem because the distinction between the two kinds of contributions involves an interchange of the limit of singular curvature with the thermodynamic limit. For all the lattices studied we found precise agreement with the conformal field theory prediction for conical singularities.

7 pages, tables and eps figures included

References in corpus (3)

• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
• Dimers and the Critical Ising Model on Lattices of genus>1
• Finite size corrections for the Ising model on higher genus triangular lattices

Cited by in corpus (6)

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• Critical behavior in spherical and hyperbolic spaces
• Geometric effects on critical behaviours of the Ising model
• The dynamic exponent of the Ising model on negatively curved surfaces
• Novel scaling behavior of the Ising model on curved surfaces
• Topological and Geometric Universal Thermodynamics in Conformal Field Theory