Extreme-Value Distributions and the Freezing Transition of Structural Glasses

We consider two mean-field models of structural glasses, the random energy model and the p-spin model (PSM), and we show that the finite-size fluctuations of the freezing temperature are described by extreme-value statistics (EVS) distributions, establishing an unprecedented connection between EVS and the freezing transition of structural glasses. For the random energy model, the freezing-temperature fluctuations are described by the Gumbel EVS distribution, while for the PSM the freezing temperature fluctuates according to the Tracy-Widom EVS distribution, which has been recently discovered within the theory of random matrices. For the PSM, we provide an analytical argument showing that the emergence of the Tracy-Widom distribution can be understood in terms of the statistics of glassy metastable states.