Simulating Lattice Spin Models on Graphics Processing Units

TL;DR

This paper demonstrates how GPU-accelerated Monte Carlo algorithms significantly speed up simulations of lattice spin models, enabling efficient study of critical phenomena and dynamical properties.

Contribution

It introduces two parallel GPU algorithms tailored for equilibrium and dynamical studies of lattice spin models, achieving substantial speedups over traditional methods.

Findings

Speedups of 70- to 150-fold with GPU implementation.

Effective simulation of critical phenomena and glass transitions.

Parallel algorithms enable large-scale and faster lattice spin simulations.

Abstract

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often the large computational effort needed when approaching critical points. In this work, it is shown how such simulations can be accelerated with the use of NVIDIA graphics processing units (GPUs) using the CUDA programming architecture. We have developed two different algorithms for lattice spin models, the first useful for equilibrium properties near a second-order phase transition point and the second for dynamical slowing down near a glass transition. The algorithms are based on parallel MC techniques, and speedups from 70- to 150-fold over conventional single-threaded computer codes are obtained using consumer-grade hardware.