Application of Simulated Tempering and Magnetizing to a Two-Dimensional Potts Model

TL;DR

This study demonstrates the effectiveness of the simulated tempering and magnetizing (STM) method in analyzing the phase transition and crossover behavior of the two-dimensional three-state Potts model under external magnetic fields across various lattice sizes.

Contribution

The paper introduces the application of STM with both temperature and external field as dynamical variables to study the 2D Potts model, enabling detailed crossover analysis.

Findings

STM effectively captures crossover behavior in the Potts model.

Simulation results agree with theoretical predictions.

Lattice size up to 160x160 was successfully analyzed.

Abstract

We applied the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to perform further investigations of the STM's applicability. The temperature as well as the external field are treated as dynamical variables updated during the STM simulations. After we obtained adequate information for several lattice sizes $L$ (up to $160\times 160$), we also performed a number of conventional canonical simulations of large lattices, especially in order to illustrate the crossover behavior of the Potts model in external field with increasing $L$. The temperature and external field for larger lattice size simulations were chosen by extrapolation of the detail information obtained by STM. We carefully analyzed the crossover scaling at the phase transitions with respect to the lattice size as well as the temperature and external field. The crossover behavior is clearly observed in the simulations in agreement with theoretical predictions.