Nonequilibrium dynamics in Ising-like models with biased initial condition,Physical Review E

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Nonequilibrium dynamics in Ising-like models with biased initial condition
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-17 , DOI: 10.1103/physreve.104.034123
Reshmi Roy ₁ , Parongama Sen ₁

Affiliation

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