Non trivial behavior of the linear response function in phase ordering kinetics

TL;DR

This paper reviews the complex behavior of the out-of-equilibrium response function during phase ordering, highlighting how dimensionality influences the scaling exponent and the breakdown of static-dynamic relations.

Contribution

It provides a comprehensive overview of the non-trivial properties of the response function in phase ordering kinetics, including analysis of the mean spherical model.

Findings

Dimensionality affects the scaling exponent $a_{\chi}$, causing static-dynamic relation failure at low dimensions.

The mean spherical model exemplifies a system where static-dynamic connection fails universally.

The response function exhibits non-trivial behavior during coarsening in phase ordering.

Abstract

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent $a_{\chi}$ which leads to failure of the connection between static and dynamic properties at the lower dimensionality $d_L$, where $a_{\chi}=0$. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.