Parallel simulation of two--dimensional Ising models using Probabilistic Cellular Automata
Abstract
We perform a numerical investigation of the \emph{shaken dynamics}, a parallel Markovian dynamics for spin systems with local interaction and whose transition probabilities depend on two parameters, and , that tune the geometry of the underlying lattice. We determine a phase transition curve, in the plane, separating the disordered phase from the ordered one, study the mixing time of the Markov chain and evaluate the spin-spin correlations as and 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.
Cite
@article{arxiv.1908.07341,
title = {Parallel simulation of two--dimensional Ising models using Probabilistic Cellular Automata},
author = {Roberto D'Autilia and Louis Nantenaina Andrianaivo and Alessio Troiani},
journal= {arXiv preprint arXiv:1908.07341},
year = {2019}
}