Nonequilibrium dynamics in Ising-like models with biased initial condition.

Abstract

We investigate the dynamical fixed points of the zero temperature Glauber dynamics in Ising-like models. The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the coordination number z in the Ising model. For the generalized voter model, a phase diagram is obtained based on this study. Numerical results for the Ising model for both the mean field case and short ranged models on lattices with different values of z are also obtained. A related study is the behavior of the exit probability E(x_{0}), defined as the probability that a configuration ends up with all spins up starting with x_{0} fraction of up spins. An interesting result is E(x_{0})=x_{0} in the mean field approximation when z=2, which is consistent with the conserved magnetization in the system. For larger values of z, E(x_{0}) shows the usual finite size dependent nonlinear behavior both in the mean field model and in the Ising model with nearest neighbor interaction on different two dimensional lattices. For such a behavior, a data collapse of E(x_{0}) is obtained using y=(x_{0}-x_{c})/x_{c}L^{1/ν} as the scaling variable and f(y)=1+tanh(λy)/2 appears as the scaling function. The universality of the exponent and the scaling factor is investigated.