A Solvable Spin-Glass of Quantum Rotors

TL;DR

This paper provides an exact solution for a model of quantum rotors with random interactions, revealing critical behavior and phase transitions that are consistent with the transverse-field Ising model.

Contribution

It offers a complete solution at infinite components and shows the critical properties are preserved at large but finite components.

Findings

Exact solution at M=∞ in spin-glass and disordered phases

Logarithmic violations of scaling at the quantum critical point

Critical properties match those of the transverse-field Ising model

Abstract

We examine a model of $M$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. A complete solution is obtained at $M=\infty$ in the spin-glass and quantum-disordered phases. The quantum phase transition separating them is found to possess logarithmic violations of scaling, with no further modifications to the leading critical behavior at any order in $1/M$; this suggests that the critical properties of the transverse-field Ising model (believed to be identical to the $M\rightarrow 1$ limit) are the same as those of the $M=\infty$ quantum rotors.