"Spherical" 3-State Potts Spin Glass: Exact Solution

TL;DR

This paper introduces an exactly solvable spherical 3-state Potts spin glass model with infinite-range interactions, utilizing random matrix theory, and confirms its results align with the replica symmetric solution.

Contribution

It presents a novel spherical version of the 3-state Potts spin glass model with an exact solution, expanding analytical tools for disordered systems.

Findings

Exact solution via random matrix theory

Results match replica symmetric approach

Provides analytical insights into spherical spin glasses

Abstract

A continuous 3-state Potts model with an analog of spherical constraints is proposed and is shown to have an exact solution in the case of infinite-ranged interactions. "Spherical" 3-state Potts spin glass model is solved using the known properties of a large random matrix. For this model the results are identical to those obtained by the replica approach for replica symmetric solution.