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.

arXiv comment5 pages, 7 figures, published in PRE Rapid communication

References in corpus (17)

• Statistical physics of social dynamics
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Minority Opinion Spreading in Random Geometry
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Coarsening and persistence in the voter model
• Fate of Zero-Temperature Ising Ferromagnets
• Freezing in Ising Ferromagnets
• Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model
• Experimental Measurement of the Persistence Exponent of the Planar Ising Model
• Dynamics of Non-Conservative Voters
• Dynamics of Vacillating Voters
• Persistence in the two dimensional ferromagnetic Ising model
• A stochastic opinion dynamics model with domain size dependent dynamic evolution
• Opinion dynamics model with weighted influence: Exit probability and dynamics
• Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents

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• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Pattern formation and coarsening dynamics in apparent competition models
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Virtual walks in spin space: a study in a family of two-parameter models
• Spatial dynamics of synergistic coinfection in rock-paper-scissors models
• Non-equilibrium dynamics in Ising like models with biased initial condition