Exactly solvable model of a quantum spin glass

TL;DR

This paper presents an exactly solvable mean field spherical spin glass model with complex interactions, exhibiting replica symmetry breaking and critical behavior similar to the SK model, and extends it to a quantum version with regular thermodynamics at low temperatures.

Contribution

It introduces an exactly solvable spherical spin glass model with multi-spin interactions and analyzes its quantum extension, providing new insights into spin glass behavior.

Findings

Model exhibits replica symmetry breaking.

Exact solution of the order parameter function.

Quantum version shows regular thermodynamics at low T.

Abstract

A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry breaking. The order parameter function is solved exactly in the whole low temperature phase. The zero field cooled susceptibility remains finite at low $T$. Next a quantum version of the system is considered. Whereas the magnetic properties are not altered qualitatively, the thermodynamics is now regular at small temperatures.