Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise

TL;DR

This paper investigates how correlated noise with power-law decay influences the critical dynamics of the  Ginzburg-Landau model, revealing non-Markovian effects on dynamic critical exponents through renormalization group analysis.

Contribution

It introduces a perturbative renormalization group approach to analyze the impact of temporal correlations in noise on critical Langevin dynamics of the  Ginzburg-Landau model, extending understanding of non-Markovian effects.

Findings

Dynamic exponents z and  are affected by noise correlations for  < _c(D,N).

Equilibrium critical exponents  and  remain unchanged by noise correlations.

Fluctuation-dissipation ratio depends on the noise correlation parameter .

Abstract

We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in space but decay as a power-law with exponent \alpha in time. These correlations are assumed to be due to the coupling to an equilibrium thermal bath. We study both the equilibrium dynamics at the critical point and quenches towards it, deriving the corresponding scaling forms and the associated equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We show that, while the first two retain their equilibrium values independently of \alpha, the non-Markovian character of the dynamics affects the dynamic exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial dimensionality, N the number of components of the order parameter, and \alpha_c(x,y) a function which we determine at second order in 4-D. We analyze the dependence of the asymptotic fluctuation-dissipation ratio on various parameters, including \alpha. We discuss the implications of our results for several physical situations.