Critical ageing correlators from Schr\"odinger-invariance

TL;DR

This paper derives the form of two-time auto-correlators and single-time correlators in critical ageing systems with dynamical exponent z=2 using Schr"odinger-invariance, matching known exact results in specific models.

Contribution

It extends Schr"odinger-invariance to non-equilibrium ageing systems and derives correlator forms that align with exact solutions in known models.

Findings

Derived correlator forms from Schr"odinger-invariance for ageing systems.

Reproduced exact results for 1D Glauber-Ising model at T=0.

Matched results for the critical spherical model in higher dimensions.

Abstract

For ageing systems, quenched onto a critical temperature $T=T_c$ such that the dominant noise comes from the thermal bath, with a non-conserved order-parameter and in addition with dynamical exponent ${z}=2$, the form of the two-time auto-correlator as well as the time-space form of the single-time correlator are derived from Schr\"odinger-invariance, generalised to non-equilibrium ageing. These findings reproduce the exact results in the $1D$ Glauber-Ising model at $T=0$ and the critical spherical model in $d>2$ dimensions.