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

TL;DR

This paper numerically investigates the universal logarithmic corrections to the free energy of the 2D Ising model at criticality, focusing on lattices with conical singularities and confirming conformal field theory predictions.

Contribution

It provides the first numerical validation of the conformal field theory predictions for logarithmic corrections due to conical singularities in the Ising model.

Findings

Precise agreement with CFT predictions for conical singularities.

Logarithmic corrections depend on the topology and singularities of the lattice.

Results extend understanding of finite-size effects in critical systems.

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.