2019/08/05 by D'Autilia, Roberto, Andrianaivo, Louis Nantenaina, Troiani, Alessio
#81T80 #82B20 #82B80 #82C20 #82C80 #Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #and Science (cs.CE)
paper · doi:10.48550/arxiv.1908.07341
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.