Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

¹ Departamento de Física, Universidade Federal do Rio Grande do Sul - CP 15051, 91501-970, Porto Alegre, Brazil
² icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS 67000 Strasbourg, France
³ FRIAS, Freiburg Institute for Advanced Studies - 79104 Freiburg, Germany

Received: 7 March 2016
Accepted: 6 June 2016

Abstract

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.