The full replica symmetry breaking solution in mean-field spin glass models
Abstract
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a well-defined formulation of the full replica symmetry breaking problem in random regular graphs. We obtain a variational free energy functional, defined by the sum of two variational functionals (auxiliary variational functionals), that are an extension of the Parisi functional of the Sherrington-Kirkpatrick model. We study the properties of the two variational functionals in detailed, providing representation through the solution of a proper backward stochastic differential equation, that generalize the Parisi partial differential equation. Finally, we define the order parameters of the system and get a set of self-consistency equations for the order parameters and free energy.
Keywords
Cite
@article{arxiv.1911.00557,
title = {The full replica symmetry breaking solution in mean-field spin glass models},
author = {Francesco Concetti},
journal= {arXiv preprint arXiv:1911.00557},
year = {2019}
}
Comments
Thesis, 2019