Replica Theory and Large D Josephson Junction Hypercubic Models

TL;DR

This paper analyzes the thermodynamic behavior of a high-dimensional Josephson junction array under magnetic fields, proposing a spin glass analogy for low-temperature properties and validating it through numerical simulations.

Contribution

It introduces a theoretical framework connecting Josephson junction models to spin glass systems and tests this conjecture with numerical simulations.

Findings

High-temperature properties are computable as D approaches infinity.

The conjectured low-temperature behavior matches simulations in certain magnetic field regimes.

The spin glass analogy is slightly inaccurate in some regimes, indicating areas for further research.

Abstract

We study the statistical mechanics of a $D$-dimensional array of Josephson junctions in presence of a magnetic field on a lattice of side $2$. In the high temperature region the thermodynamical properties can be computed in the limit $D \to \infty$. A conjectural form of the thermodynamic properties in the low temperature phase is obtained by assuming that they are the same of an appropriate spin glass system, based on quenched disordered couplings. Numerical simulations show that this conjecture is very accurate in one regime of the magnetic field, while it is probably slightly inaccurate in a second regime.