Response of non-equilibrium systems with long-range initial correlations

TL;DR

This paper investigates the long-time dynamics of the spherical model with long-range initial correlations, revealing multiple aging behaviors at criticality and the influence of initial conditions on autocorrelation and response exponents.

Contribution

It provides exact calculations of two-time functions and identifies five types of aging at criticality based on initial correlations, extending understanding of non-equilibrium dynamics.

Findings

Five distinct aging types at criticality depending on initial correlations

Autocorrelation and response exponents depend on initial conditions

Scaling forms align with local scale invariance predictions

Abstract

The long-time dynamics of the $d$-dimensional spherical model with a non-conserved order parameter and quenched from an initial state with long-range correlations is studied through the exact calculation of the two-time autocorrelation and autoresponse functions. In the aging regime, these are given in terms of non-trivial universal scaling functions of both time variables. At criticality, five distinct types of aging are found, depending on the form of the initial correlations, while at low temperatures only a single type of aging exists. The autocorrelation and autoreponse exponents are shown to be generically different and to depend on the initial conditions. The scaling form of the two-time response functions agrees with a recent prediction coming from local scale invariance.