Self-Organized Criticality in Optimistic Simulation of Correlated Systems

Abstract

A variety of slowly driven diffusive systems have been shown to self organize into a critical state. In this paper we study the dynamic runtime behavior of the optimistic parallel Time Warp simulation method. The method is based on an asynchronous execution of timed events. The basic problem is the out of order execution of events. A causality error results in so-called rollback of processed events until the causality error is resolved. By using the Ising spin model we show experimentally that the distribution of number of rolled back events behaves as a power-law distribution over a large range of sub-critical Ising temperatures and decays exponentially above for super-critical Ising temperatures. For critical Ising temperatures, the computational complexity of Time Warp and physical complexity of the Ising spin model are entangled and contribute both to the runtime behavior in a non-linear way.