The role of initial conditions in the ageing of the long-range spherical model

TL;DR

This paper investigates how initial conditions influence the aging dynamics of the long-range spherical model, revealing conditions under which aging behavior depends or becomes independent of initial states.

Contribution

It provides explicit conditions for the crossover between initial-condition-dependent and independent aging regimes in the long-range spherical model.

Findings

Aging exponents depend on initial state features.

Explicit crossover conditions between aging regimes.

Analysis of auto-correlation and response functions.

Abstract

The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not.