GPU-based single-cluster algorithm for the simulation of the Ising model

TL;DR

This paper introduces a GPU-based implementation of the Wolff single-cluster algorithm for the Ising model, achieving significant speedups over CPU calculations and proposing a quasi-block synchronization method applicable to various parallel computations.

Contribution

The paper presents a novel GPU algorithm with quasi-block synchronization for the Ising model, significantly enhancing simulation speed and broadening parallel computation techniques.

Findings

GPU speedup of 5.60x for 2D Ising at L=4096

GPU speedup of 7.90x for 3D Ising at L=256

Quasi-block synchronization applicable to various fields

Abstract

We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L=4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L=256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.