Non-equilibrium 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 generalised 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 behaviour 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 magnetisation in the system. For larger values of $z$, $E(x_0)$ shows the usual finite size dependent non linear behaviour both in the mean field model and in Ising model with nearest neighbour interaction on different two dimensional lattices. For such a behaviour, a data collapse of $E(x_0)$ is obtained using $y=\frac{(x_0-x_c)}{x_c}{L}^{1/\nu }$ as the scaling variable and $f(y)=\frac{1+\tanh (\lambda y)}{2}$ appears as the scaling function. The universality of the exponent and the scaling factor is investigated.

arXiv comment9 pages, 14 figures

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