Critical slowing down in Ising model for Creutz algorithm

Dynamical critical exponents for the two dimensional Ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto-correlation functions for the order parameter and the internal energy at the critical temperatures, and from the nonlinear relaxation time for the order parameter near the critical temperature. The analysis of the data within the frame of the dynamical finite size scaling hypothesis gives ZM=ZE=2.20 and ZAM=1.91 and ZAE=0.19 for the linear dynamical exponents corresponding, respectively, to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy, and ΔnlM=2.07 for the nonlinear dynamical exponent for the order parameter. These values verify the scaling relations between the dynamical exponents.