Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry

TL;DR

This paper investigates the ground state and spin glass phase of the large N infinite range spin glass, revealing differences from spherical models, the role of the number of spin components, and introducing a supersymmetric formalism for disorder averaging.

Contribution

It develops a supersymmetric formalism to analyze the large N spin glass, highlighting differences from spherical models and examining the effects of spin components on the ground state.

Findings

Identifies the number of spin components needed for the ground state.

Discovers a slight increase in ground state energy compared to naive expectations.

Finds level repulsion similar to random matrix theory persists in the interacting system.

Abstract

The large N infinite range spin glass is considered, in particular the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical significance of k for the correlation functions is discussed. The difference between the large N and spherical spin glass is emphasized; a slight difference between the average Lagrange multiplier of the large N and spherical spin glasses is derived, leading to a slight increase in the energy of the ground state compared to the naive expectation. Further, there is a change in the low energy density of excitations in the large N system. A form of level repulsion, similar to that found in random matrix theory, is found to exist in this system, surviving interactions. Even though the system is an interacting one, a supersymmetric formalism is developed to deal with the problem of averaging over disorder.