C-Periodicity and the Physical Mass in the 3-State Potts Model

TL;DR

This paper demonstrates a Monte Carlo simulation method for the 3-state Potts model that uses C-periodic boundary conditions to accurately define correlation functions and particle mass without bias or translation invariance issues.

Contribution

It introduces a C-periodic boundary condition approach for Monte Carlo simulations of the 3-state Potts model, improving the accuracy of correlation and mass measurements.

Findings

Successful implementation on a 24x24x48 lattice

Avoids phase-dependent biases in data evaluation

Maintains translation invariance in simulations

Abstract

The standard infinite-volume definition of connected correlation function and particle mass in the 3-state Potts model can be implemented in Monte Carlo simulations by using C-periodic spatial boundary conditions. This avoids both the breaking of translation invariance (cold wall b.c.) and the phase-dependent and thus possibly biased evaluation of data (periodic boundary cconditions). The numerical feasibility of the standard definitions is demonstrated by sample computations on a 24*24*48 lattice.