Parallel Cluster Labeling for Large-Scale Monte Carlo Simulations

TL;DR

This paper introduces an optimized parallel cluster labeling algorithm for large-scale Monte Carlo simulations, achieving high efficiency and enabling the study of large spin systems with detailed analysis of relaxation dynamics.

Contribution

The paper presents a novel parallel cluster labeling algorithm that improves speed and efficiency for large-scale Monte Carlo simulations on supercomputers.

Findings

Achieved simulation of 65536 x 65536 spin systems at 11 ns/site

Demonstrated good speed-up and efficiency in parallel processing

Identified exponential and power-law relaxation behaviors in large Ising models

Abstract

We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with large numbers of processors. The algorithm divides physical space into rectangular cells which are assigned to processors and combines a serial local labeling procedure with a relaxation process across nearest-neighbor processors. By controlling overhead and reducing inter-processor communication this method attains good computational speed-up and efficiency. Large systems of up to 65536 X 65536 spins have been simulated at updating speeds of 11 nanosecs/site (90.7 million spin updates/sec) using state-of-the-art supercomputers. In the second part of the article we use the cluster algorithm to study the relaxation of magnetization and energy on large Ising models using Swendsen-Wang dynamics. We found evidence that exponential and power law factors are present in the relaxation process as has been proposed by Hackl et al.