Novel Monte Carlo method to calculate the central charge and critical exponents

TL;DR

This paper introduces a new finite size scaling Monte Carlo method that enables direct calculation of the central charge and critical exponents in two-dimensional critical systems by analyzing the stress tensor's behavior.

Contribution

The paper presents a novel Monte Carlo finite size scaling technique focusing on the stress tensor to determine central charge and critical exponents directly.

Findings

Method successfully applied to Ising, Ashkin-Teller, and F-models.

Stress tensor is insensitive to critical slowing down.

Allows direct calculation of central charge from Monte Carlo simulations.

Abstract

A typical problem with Monte Carlo simulations in statistical physics is that they do not allow for a direct calculation of the free energy. For systems at criticality, this means that one cannot calculate the central charge in a Monte Carlo simulation. We present a novel finite size scaling technique for two-dimensional systems on a geometry of LxM, and focus on the scaling behavior in M/L. We show that the finite size scaling behavior of the stress tensor, the operator that governs the anisotropy of the system, allows for a determination of the central charge and critical exponents. The expectation value of the stress tensor can be calculated using Monte Carlo simulations. Unexpectedly, it turns out that the stress tensor is remarkably insensitive for critical slowing down, rendering it an easy quantity to simulate. We test the method for the Ising model (with central charge c=1/2), the Ashkin-Teller model (c=1), and the F-model (also c=1).