Interplay of interfacial noise and curvature driven dynamics in two dimensions

Abstract

We explore the effect of interplay of interfacial noise and curvature driven dynamics in a binary spin system. An appropriate model is the generalised two dimensional voter model proposed earlier (J. Phys. A: Math. Gen. {\bf 26}, 2317 (1993)), where the flipping probability of a spin depends on the state of its neighbours and is given in terms of two parameters $x$ and $y$. $x=0.5,y=1$ corresponds to the conventional voter model which is purely interfacial noise driven while $x=1$ and $y=1$ corresponds to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for $0.5<x<1$ keeping $y=1$ is studied in detail. The dynamical behaviour of the relevant quantities show characteristic differences from both $x=0.5$ and $1$. The most remarkable result is the existence of two time scales for $x\ge x_c$ where $x_c\approx 0.7$. On the other hand, we have studied the exit probability which shows Ising like behaviour with an universal exponent for any value of $x>0.5$; the effect of $x$ appears in altering the value of the parameter occurring in the scaling function only.

5 pages, 7 figures, published in PRE Rapid communication

References in corpus (5)

• Statistical physics of social dynamics
• Dynamics of Non-Conservative Voters
• Dynamics of Vacillating Voters
• Persistence in the two dimensional ferromagnetic Ising model
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents

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• Pattern formation and coarsening dynamics in apparent competition models
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Spatial dynamics of synergistic coinfection in rock-paper-scissors models
• Non-equilibrium dynamics in Ising like models with biased initial condition