The m-component spin glass on a Bethe lattice

TL;DR

This paper investigates the m-component vector spin glass model on a Bethe lattice using the cavity method, revealing a generalized Bose-Einstein condensation and scaling relations near the phase transition.

Contribution

It provides a self-consistent solution for the model in the infinite-component limit and analyzes the low-temperature phase with numerical methods.

Findings

Identification of a generalized Bose-Einstein condensation

Scaling relations between zero-temperature exponents

Numerical analysis of the low-temperature phase

Abstract

We study the m-component vector spin glass in the limit m to infinity on a Bethe lattice. The cavity method allows for a solution of the model in a self-consistent field approximation and for a perturbative solution of the full problem near the phase transition. The low temperature phase of the model is analyzed numerically and a generalized Bose-Einstein condensation is found, as in the fully connected model. Scaling relations between four distinct zero-temperature exponents are found.