Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

TL;DR

This study investigates the non-equilibrium dynamics of the 4D spherical model at its upper critical dimension, revealing the absence of logarithmic corrections in its aging scaling functions and confirming the domain growth law L(t) ~ t^0.5.

Contribution

It demonstrates that, contrary to expectations, the aging behavior in the 4D spherical model lacks logarithmic scaling corrections at the upper critical dimension.

Findings

Scaling functions lack logarithmic corrections

Domain size scales as L(t) ~ t^0.5

Aging behavior consistent with mean-field predictions

Abstract

The non-equilibrium dynamics of the kinetic spherical model, quenched to T<=T_c, with a non-conserved order-parameter is studied at its upper critical dimension d=d*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t) ~ t^0.5 .