Freezing and low temperature entropy: The case of mean-field Gaussian model

Abstract

The freezing phenomenon is studied in connection with the low temperature behavior of the entropy of the Gibbs measure. In particular, in the case of the mean-field Gaussian spin-glass model, from the study of a functional relation between the free energies at two different temperatures, we show that the maximum value of the inverse temperature beyond which the specific entropy of the Gibbs measure cannot be strictly positive is given by β* = 4 log 2. The low temperature entropy of the random energy model is also discussed.