Aging, phase ordering and conformal invariance

TL;DR

This paper explores how aging systems' response functions can be extended to conformal invariance, providing explicit scaling functions validated through numerical and exact results across various spin models.

Contribution

It extends dynamical scaling to conformal invariance in aging systems, deriving explicit scaling functions and confirming them with numerical and exact solutions.

Findings

Conformal invariance extends dynamical scaling in aging systems.

Explicit scaling functions are confirmed in multiple spin models.

Results include numerical studies of 2D and 3D Ising models and exact solutions for spherical models.

Abstract

In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the scaling function $f$. This quantitative prediction is confirmed in several spin systems, both for $T<T_c$ (phase ordering) and $T=T_c$ (non-equilibrium critical dynamics). The 2D and 3D Ising models with Glauber dynamics are studied numerically, while exact results are available for the spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.