To maximize or not to maximize the free energy of glassy systems, !=?

TL;DR

This paper investigates the role of free energy maximization versus marginality criteria in glassy systems, revealing that in replica calculations, the free energy is minimized, leading to first-order phase transitions at the dynamic transition point.

Contribution

It demonstrates that in replica calculations, the marginality criterion minimizes free energy, contrasting with the maximization condition in static analysis, and clarifies the thermodynamic implications.

Findings

In replica calculations, the marginality criterion minimizes free energy.

First order phase transitions occur at the dynamic transition point.

Thermodynamics differs from long-time dynamical analysis despite similar order parameters.

Abstract

The static free energy of glassy systems can be expressed in terms of the Parisi order parameter function. When this function has a discontinuity, the location of the step is determined by maximizing the free energy. In dynamics a transition is found at larger temperature, while the location of the step satisfies a marginality criterion. It is shown here that in a replica calculation this criterion minimizes the free energy. This leads to first order phase transitions at the dynamic transition point. Though the order parameter function is the same as in the long-time limit of a dynamical analysis, thermodynamics is different.