Two-loop Critical Fluctuation-Dissipation Ratio for the Relaxational Dynamics of the O(N) Landau-Ginzburg Hamiltonian

TL;DR

This paper calculates the two-loop fluctuation-dissipation ratio for the critical dynamics of the O(N) Landau-Ginzburg model, revealing universal aging behavior at criticality.

Contribution

It provides a two-loop perturbative analysis of the fluctuation-dissipation ratio in the critical O(N) model, extending previous one-loop results.

Findings

Derived the universal scaling functions for response and correlation

Computed the fluctuation-dissipation ratio at two-loop order

Identified nontrivial aging behavior at criticality

Abstract

The off-equilibrium purely dissipative dynamics (Model A) of the O(N) vector model is considered at criticality in an $\epsilon = 4- d > 0$ up to O($\epsilon^2$). The scaling behavior of two-time response and correlation functions at zero momentum, the associated universal scaling functions, and the nontrivial limit of the fluctuation-dissipation ratio are determined in the aging regime.