A Multispin Algorithm for the Kob-Andersen Stochastic Dynamics on Regular Lattices

TL;DR

This paper introduces a multispin coding algorithm tailored for simulating Kob-Andersen glassy dynamics on regular lattices, enhancing computational efficiency and enabling exploration of phase transitions in complex spin systems.

Contribution

The paper develops a novel multispin coding algorithm for Kob-Andersen dynamics, extending it to random regular graphs and demonstrating its effectiveness through numerical simulations.

Findings

Algorithm significantly speeds up simulations.

Identifies transition points in the model.

Provides detailed numerical results.

Abstract

The aim of the paper is to propose an algorithm based on the Multispin Coding technique for the Kob-Andersen glassy dynamics. We first give motivations to speed up the numerical simulation in the context of spin glass models [M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)], after defining the Markovian dynamics as in [W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993)] as well as the related interesting observables, we extend it to the more general framework of random regular graphs, listing at the same time some known analytical results [C. Toninelli, G. Biroli, D.S. Fisher, J. Stat. Phys. 120, 167 (2005)]. The purpose of this work is a dual one, firstly, we describe how bitwise operators can be used to build up the algorithm by carefully exploiting the way data are stored on a computer. Since it was first introduced [M. Creutz, L. Jacobs, C. Rebbi, Phys. Rev. D 20, 1915 (1979), C. Rebbi, R.H. Swendsen, Phys. Rev. D 21, 4094 (1980)], this technique has been widely used to perform Monte Carlo simulations for Ising and Potts spin systems, however, it can be successfully adapted to more complex systems in which microscopic parameters may assume boolean values. Secondly, we introduce a random graph in which a characteristic para- meter allows to tune the possible transition point. A consistent part is devoted to listing the numerical results obtained by running numerical simulations.