Crossover scaling in the two-dimensional three-state Potts model

TL;DR

This study uses advanced Monte Carlo simulations to analyze the crossover scaling behavior of the 2D three-state Potts model under external magnetic fields, revealing transitions between different universality classes.

Contribution

It introduces a comprehensive simulation approach combining simulated tempering and magnetizing techniques to explore crossover phenomena in the Potts model.

Findings

Identified crossover behavior from Potts to Ising universality class.

Performed finite-size scaling analysis across various lattice sizes.

Provided detailed phase diagram in temperature-field space.

Abstract

We apply simulated tempering and magnetizing (STM) Monte Carlo simulations to the two-dimensional three-state Potts model in an external magnetic field in order to investigate the crossover scaling behaviour in the temperature-field plane at the Potts critical point and towards the Ising universality class for negative magnetic fields. Our data set has been generated by STM simulations of several square lattices with sizes up to 160 x 160 spins, supplemented by conventional canonical simulations of larger lattices at selected simulation points. We present careful scaling and finite-size scaling analyses of the crossover behaviour with respect to temperature, magnetic field and lattice size.