The phenomenon of spontaneous replica symmetry breaking in complex statistical mechanics systems

Abstract

We analyze the main aspects of the phenomenon of spontaneous replica symmetry breaking, introduced by Giorgio Parisi. We work in the frame of real replicas, by taking into account the simple case of the random energy model. In particular, we study the phase space diagram for systems of coupled replicas, and the connected phase transitions. Our considerations can be generalized to the more complicated models of mean field spin glasses and neural networks. We report also about a letter of Ettore Majorana, written in December 1937 to his uncle Dante, very interesting for its methodological content.