Estimation of the central charge by Monte Carlo simulations

Abstract

Using an idea put forward by J.L. Cardy, we demonstrate how to obtain a good estimate for the central charge c of a conformally invariant field theory by Monte Carlo simulations of the corresponding statistical model away from critically, but in the scaling region; the two-dimensional three-state Potts model in a magnetic field is used as a test case. Determining c in this way has become feasible because of a big increase in the availability of computational power and because of the invention of stochastic cluster algorithms, which allow an efficient simulation of statistical models near criticality. This method provides a reliable way to determine c for models, for which the other known methods have failed up to now.