Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state

TL;DR

This paper investigates the non-equilibrium critical relaxation dynamics of ferromagnetic vector models with O(n) symmetry, focusing on fluctuation-dissipation ratios and crossover behaviors from different initial states.

Contribution

It provides exact solutions for Gaussian fluctuations and first-order epsilon-expansion results for non-Gaussian effects in the relaxation process.

Findings

FDRs differ for longitudinal and transverse modes at Gaussian level

Complete description of crossover from short-time to long-time behavior

Reliable 3D estimates of fluctuation-dissipation ratios

Abstract

Within the universality class of ferromagnetic vector models with O(n) symmetry and purely dissipative dynamics, we study the non-equilibrium critical relaxation from a magnetized initial state. Transverse correlation and response functions are exactly computed for Gaussian fluctuations and in the limit of infinite number n of components of the order parameter. We find that the fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes differ already at the Gaussian level. In these two exactly solvable cases we completely describe the crossover from the short-time to the long-time behavior, corresponding to a disordered and a magnetized initial condition, respectively. The effects of non-Gaussian fluctuations on longitudinal and transverse quantities are calculated in the first order in the epsilon-expansion and reliable three-dimensional estimates of the two FDRs are obtained.