Simplified dynamics for glass model

TL;DR

This paper introduces a simplified, phenomenological dynamic model for glass systems based on a hierarchy of order parameters and a truncated Langevin approach, aiming to better understand relaxation and phase transitions.

Contribution

It proposes a new simplified dynamic framework for glass models using a hierarchy of order parameters and a truncated Langevin approximation, extending mean field statics.

Findings

Identification of trap points in phase space

Analysis of kinetical phase transitions

Development of a phenomenological relaxation process

Abstract

In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system phenomonologically, as exchange of energy between 2 parts. It is possible to identify trap points in phase space. We suggest some phenomonological approximation-truncated Langevine. The mean field statics is used to introduce a phenomenologic dynamics as its natural extension. Purely kinetical phase transitions are investigated..