Cluster vs Single-Spin Algorithms -- Which are More Efficient?

TL;DR

This paper compares the efficiency of single-cluster and single-spin algorithms for the 2D and 3D Ising model, finding that cluster algorithms become more efficient at large system sizes, with crossover points depending on computer type.

Contribution

It provides a systematic comparison of algorithm efficiency based on computational time to achieve statistical accuracy, highlighting the size-dependent crossover point.

Findings

Cluster algorithms are more efficient for large systems.

Crossover size depends on computer type.

Efficiency advantage appears at system sizes above 70-300 in 2D and 80-200 in 3D.

Abstract

A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms of site updates per second or the dynamical critical exponents. Our main result is that the cluster algorithms become more efficient when the system size, $L^d$, exceeds, $L\sim 70$--$300$ for $d=2$ and $L\sim 80$--$200$ for $d=3$. The exact value of the crossover is dependent upon the computer being used. The lower end of the crossover range is typical of workstations while the higher end is typical of vector computers. Hence, even for workstations, the system sizes needed for efficient use of the cluster algorithm is relatively large.