q-State Potts model metastability study using optimized GPU-based Monte Carlo algorithms

TL;DR

This paper presents a GPU-accelerated Monte Carlo simulation method for the 2D q-state Potts model, enabling large-scale studies of metastability with significant speedup over CPU implementations.

Contribution

The authors developed an optimized GPU-based Monte Carlo algorithm for large-scale Potts model simulations, demonstrating high efficiency and enabling metastability analysis on unprecedented system sizes.

Findings

Confirmed the existence of metastability in large systems using Binder's criterion.

Achieved up to 155x speedup compared to CPU code.

Simulated systems with up to 10^9 spins.

Abstract

We implemented a GPU based parallel code to perform Monte Carlo simulations of the two dimensional q-state Potts model. The algorithm is based on a checkerboard update scheme and assigns independent random numbers generators to each thread. The implementation allows to simulate systems up to ~10^9 spins with an average time per spin flip of 0.147ns on the fastest GPU card tested, representing a speedup up to 155x, compared with an optimized serial code running on a high-end CPU. The possibility of performing high speed simulations at large enough system sizes allowed us to provide a positive numerical evidence about the existence of metastability on very large systems based on Binder's criterion, namely, on the existence or not of specific heat singularities at spinodal temperatures different of the transition one.