Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems

TL;DR

This paper extends a parallel kinetic Monte Carlo algorithm to large-scale 3D Ising models, demonstrating accurate, scalable simulations of billion-atom systems and calculating critical exponents with high fidelity.

Contribution

The paper introduces a synchronized parallel KMC algorithm for large 3D lattices, ensuring statistical validity and efficient scaling for billion-atom simulations.

Findings

Algorithm scales well with problem size and sublattice partition

Bias from sublattice decomposition is within statistical error

Critical exponents match state-of-the-art simulations

Abstract

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial method, which confirms the statistical validity of the method. We have assessed the parallel efficiency of the method and find that our algorithm scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations.