Asynchronously parallelised percolation on distributed machines

TL;DR

This paper introduces an asynchronous parallel method for simulating percolation on distributed systems, enabling high-precision measurements on large lattices with minimal hardware requirements.

Contribution

It presents a novel asynchronous parallel implementation of the Hoshen-Kopelman algorithm for large-scale percolation simulations on distributed machines.

Findings

Nonuniversal constants in the scaling function satisfy a scaling relation.

Moment ratios for the largest cluster reveal a characteristic aspect ratio.

Method achieves high precision on large lattices with low hardware demands.

Abstract

We propose a powerful method based on the Hoshen-Kopelman algorithm for simulating percolation asynchronously on distributed machines. Our method demands very little of hardware and yet we are able to make high precision measurements on very large lattices. We implement our method to calculate various cluster size distributions on large lattices of different aspect ratios spanning three orders of magnitude for two-dimensional site and bond percolation. We find that the nonuniversal constants in the scaling function for the cluster size distribution apparently satisfy a scaling relation, and that the moment ratios for the largest cluster size distribution reveal a characteristic aspect ratio at r approx. 9.