Off equilibrium dynamics in the 3d-XY system

TL;DR

This study uses Monte Carlo simulations to analyze the non-equilibrium dynamics of the 3D XY-model after a quench, focusing on autocorrelation, response functions, and fluctuation-dissipation ratios in different phases.

Contribution

It provides detailed numerical analysis of non-equilibrium exponents and confirms the local scale-invariance prediction for the 3D XY-model.

Findings

The scaling function matches local scale-invariance predictions.

The fluctuation-dissipation ratio vanishes in the ordered phase.

The fluctuation-dissipation ratio approaches 0.43 at criticality.

Abstract

We investigate through Monte Carlo simulations the non-equilibrium behaviour of the three-dimensional XY-model quenched from a high temperature state to its ferromagnetic and critical phases. The two-times autocorrelation and response functions are determined in the asymptotic (scaling) regime, from which the nonequilibrium exponents $\lambda$ and critical $\lambda^c$ are extracted. The form of the scaling function is in agreement with the prediction of local scale-invariance. The so-called limit fluctuation-dissipation ratio $X_\infty$ is shown to vanish in the ordered phase and to reach a constant value around 0.43 for the critical quench.