Algebraic coarsening in voter models with intermediate states

Details Algebraic coarsening in voter models with intermediate states Algebraic coarsening in voter models with intermediate states

2008-06-04

arxiv.org/abs/0806.0817v2

Physics

Condensed Matter

Statistical Mechanics

11 pages, 5 figures; minor typos corrected

Scientific paper

10.1088/1751-8113/41/43/435003

The introduction of intermediate states in the dynamics of the voter model modifies the ordering process and restores an effective surface tension. The logarithmic coarsening of the conventional voter model in two dimensions is eliminated in favour of an algebraic decay of the density of interfaces with time, compatible with Model A dynamics at low temperatures. This phenomenon is addressed by deriving Langevin equations for the dynamics of appropriately defined continuous fields. These equations are analyzed using field theoretical arguments and by means of a recently proposed numerical technique for the integration of stochastic equations with multiplicative noise. We find good agreement with lattice simulations of the microscopic model.

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