Time-dependent critical properties of Ising models by damage spreading

We use the method of damage spreading to study the time, t, taken for a spin at a distance r to be damaged for the first time in Ising models with heat-bath dynamics. We report time-dependent scaling exponents, dt ≃ 2.0 (1D), 2.52 (2D), 2.26 (3D) and (2.0) (4D), if we assume that t ∾ rdt. We also analyze our data assuming various forms of logarithmic corrections and we find that dt ∾ 2.25 or less (2D) and ∾2.0 (3D). We argue that it is extremely plausible that dt is equal to z, the dynamic critical exponent, and thus our estimate of z, in two dimensions is higher than the “consensus” value of 2.14, but we find good agreement in one, three and four dimensions with the exact and expected values.