Fragility in p-spin models

TL;DR

This paper explores the relationship between fragility and phase space properties in the p-spin model, revealing new insights into the correlation between vibrational properties, state distribution, and transition paths in glassy systems.

Contribution

It provides a detailed analysis of fragility in the p-spin model, showing the correlation with vibrational properties and the inverse relationship between the number of states and fragility, along with a geometric phase space interpretation.

Findings

Fragility correlates with vibrational properties at low temperature.

Number of states decreases as fragility increases.

Transition paths significantly influence fragility.

Abstract

We investigate the relation between fragility and phase space properties - such as the distribution of states - in the mean field p-spin model, a solvable model that has been frequently used in studies of the glass transition. By direct computation of all the relevant quantities, we find that: i) the recently observed correlation between fragility and vibrational properties at low temperature is present in this model; ii) the total number of states is a decreasing function of fragility, at variance of what is currently believed. We explain these findings by taking into account the contribution to fragility coming from the transition paths between different states. Finally, we propose a geometric picture of the phase space that explains the correlation between properties of the transition paths, distribution of states and their vibrational properties. However, our analysis may not apply to strong systems where inflection points in the configurational entropy as a function of the temperature are found.