Effective equilibrium picture in $xy-$model with exponentially correlated noise

Matteo Paoluzzi; Umberto Marini Bettolo Marconi; Claudio Maggi

doi:10.1103/physreve.97.022605

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arXiv · 1709.04232

Effective equilibrium picture in $xy-$model with exponentially correlated noise

Matteo Paoluzzi·Umberto Marini Bettolo Marconi·Claudio Maggi

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Abstract

We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of the non-equilibrium dynamics into an effective equilibrium theory. In mean-field, the critical temperature increases with the noise correlation time $τ$ indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

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Matteo Paoluzzi, Umberto Marini Bettolo Marconi, Claudio Maggi. 2018-01-18. Effective equilibrium picture in $xy-$model with exponentially correlated noise. https://doi.org/10.1103/physreve.97.022605

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