Fragility in p-spin models

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.

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• Why liquids are fragile
• Activated events in glasses: the structure of entropic droplets
• Replica theory for fluctuations of the activation barriers in glassy systems
• Topological properties of the mean field phi^4 model
• Equilibrium Fluctuations in Mean-field Disordered Models
• A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models