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Effective equilibrium picture in the xy model with exponentially correlated noise
Matteo Paoluzzi1, Umberto Marini Bettolo Marconi2,3, Claudio Maggi4
1Department of Physics and Syracuse Soft & Living Matter Program, Syracuse University, Syracuse, New York 13244, USA.
Abstract:
We study the effect of exponentially correlated noise on the xy model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the 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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