Parallel simulation of two--dimensional Ising models using Probabilistic Cellular Automata

Abstract

We perform a numerical investigation of the shaken dynamics, a parallel Markovian dynamics for spin systems with local interaction and whose transition probabilities depend on two parameters, q and J, that tune the geometry of the underlying lattice. We determine a phase transition curve, in the (q, J) plane, separating the disordered phase from the ordered one, study the mixing time of the Markov chain and evaluate the spin-spin correlations as q and J vary. Further, we investigate the relation between the equilibrium measure of the shaken dynamics and the Gibbs measure for the Ising model. Two different approaches are considered for the implementation of the dynamics: a multicore CPU approach, with code written in Julia and a GPU approach with code written in CUDA.