Energy landscape and rigidity

TL;DR

This paper investigates how floppy modes influence thermodynamical properties and energy landscape topology in glasses, proposing a modified Debye model and linking rigidity to landscape features to explain glass transition phenomena.

Contribution

It introduces a modified Debye model accounting for floppy modes and relates energy landscape topology to rigidity, providing insights into glass transition features.

Findings

Floppy modes are not at zero frequency, affecting thermodynamics.

A modified Debye model predicts deviations at low temperatures.

The model explains features like specific heat jumps in glasses.

Abstract

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes with the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This allows to understand certains features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.