Effective temperature in the quench of coarsening systems to and below $T_C$

TL;DR

This paper reviews the scaling behavior of effective temperature in quenched non-disordered systems like ferromagnets, focusing on how dimensionality affects asymptotic properties and clarifying distinctions between different quench scenarios.

Contribution

It provides a comprehensive analysis of effective temperature behavior across various dimensions and clarifies the nature of quenches to zero temperature at lower critical dimensions.

Findings

Effective temperature scaling varies with dimensionality.

Quench to $T_C=0$ at lower critical dimension is not a critical quench.

Implications for aging response exponent $a$ below $T_C$.

Abstract

We overview the general scaling behavior of the effective temperature in the que nches of simple non disordered systems, like ferromagnets, to and below $T_C$. Emphasis is on the behavior as d imensionality is varied. Consequences on the shape of the asymptotic parametric representation are derived. In particu lar, this is always trivial in the critical quenches with $T_C>0$. We clarify that the quench to $T_C=0$ at the lower critical dimensionality $d_L$, cannot be regarded as a critical quench. Implications for the behavior of the exponent $a$ of the aging response function in the quenches below $T_C$ are developed.