Understanding Spin Glass Systems

Abstract

In this thesis, we estimate the average ground state energy of spin glass models. Despite decades of study, there have been no exact explicit calculations for a mean field model of spin glass with finite ranged interactions. In the first part of the thesis we attempt to estimate the average ground state energy of the Sherrington Kirkpatrick model and the disordered Ising model on a random regular graph by numerical and analytic methods. We attempt to find the ground state energy by several methods such as Greedy algorithm, using Eigenvector ansatz, the cluster flip algorithm and subsequently make improvements on it. We also study the spectral properties of random regular graphs using Random Layered locally Tree like Lattice (RLTL) and compare the results to the predictions from random matrix theory.