Finite Size Corrections to Disordered Systems : mean field results and applications to finite dimensional models

TL;DR

This thesis investigates finite size effects in disordered systems using mean field approaches and applies these methods to various finite-dimensional models, providing new insights into their behavior.

Contribution

It develops a framework for calculating finite size corrections in disordered systems and applies it to models like the random field Ising model and Euclidean optimization problems.

Findings

Finite size corrections are quantified for disordered models.

Mean field results are extended to finite-dimensional systems.

Applications include the random field Ising model and Euclidean problems.

Abstract

This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Corrections On Random Graphs; Chapter 5 - The Random Field Ising Model; Chapter 6 - The Euclidean Assignment Problem; Chapter 7 - The Euclidean Matching Problem; Chapter 8 - The Large M Expansion.