Overlap fluctuations from the Boltzmann random overlap structure

Abstract

We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Overlap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and co-workers, who developed a variational approach to the Sherrington-Kirkpatrick model. Here we propose an iterative procedure to show that, in the so-called Boltzmann ROSt, Aizenman-Contucci polynomials naturally arise for almost all values of the inverse temperature (not in average over some interval only). These polynomials impose restrictions on the overlap fluctuations in agreement with Parisi theory.