Determination of CFT central charge by the Wang-Landau algorithm

TL;DR

This paper introduces a Monte Carlo simulation method using the Wang-Landau algorithm to accurately estimate the central charge of conformal field theories at critical points of 2D lattice models.

Contribution

The paper presents a novel approach to determine the CFT central charge from free energy scaling using the Wang-Landau algorithm, applicable to various lattice models.

Findings

Accurate central charge estimation for Ising and Potts models.

Method successfully applied to tricritical and diluted Ising models.

Discussion on estimating conformal weights.

Abstract

We propose a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with a good precision from a free energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts and site-diluted Ising models, and also discuss estimation of conformal weights.