Generic features of the fluctuation dissipation relation in coarsening systems

TL;DR

This paper investigates the fluctuation dissipation relation in coarsening systems across various dimensions, revealing that a key exponent vanishes at the lower critical dimension, indicating universal features of phase ordering.

Contribution

It provides a unified phenomenological formula for the dimensionality dependence of response function exponents in phase-ordering systems.

Findings

The exponent $a_\chi$ vanishes as dimension approaches the lower critical dimension.

A non-trivial fluctuation dissipation relation exists at the lower critical dimension.

The connection between statics and dynamics breaks down at the lower critical dimension.

Abstract

The integrated response function in phase-ordering systems with scalar, vector, conserved and non conserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution $\chi_{ag} (t,t_w)= t_w ^{-a_\chi} \hat \chi (t/t_w)$ we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of $a_\chi$ in all cases considered. The primary result is that $a_\chi$ vanishes continuously as $d$ approaches the lower critical dimensionality $d_L$. This implies that i) the existence of a non trivial fluctuation dissipation relation and ii) the failure of the connection between statics and dynamics are generic features of phase ordering at $d_L$.