$D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators

TL;DR

This paper analyzes the thermodynamics of a D-dimensional Josephson junction array under magnetic fields, revealing connections to spin glasses and q-deformed harmonic oscillators, especially near phase transitions.

Contribution

It introduces a mean field approach to study high-dimensional Josephson junction arrays and links their behavior to gauge glasses and q-deformed oscillators.

Findings

High-temperature properties simplified in the D→∞ limit.

Close to transition, system resembles gauge glasses.

Mapping coefficients to q-deformed harmonic oscillator matrix elements.

Abstract

We study the statistical mechanics of a $D$-dimensional array of Josephson junctions in presence of a magnetic field. In the high temperature region the thermodynamical properties can be computed in the limit $D \to \infty$, where the problem is simplified; this limit is taken in the framework of the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e. to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the $q$-deformed harmonic oscillator.