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

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.

References in corpus (1)

• Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation

Cited by in corpus (19)

• A tentative Replica Study of the Glass Transition
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials
• Chaos on the hypercube
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Replica Theory and Large D Josephson Junction Hypercubic Models
• Solving the Frustrated Spherical Model with q-Polynomials
• Slow Dynamics in Glasses
• Zero-temperature resistive transition in Josephson-junction arrays at irrational frustration
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Area versus Length Distribution for Closed Random Walks
• Compound real Wishart and q-Wishart matrices
• Frustrated magnets in the limit of infinite dimensions: dynamics and disorder-free glass transition
• Classical and Quantum Behavior in Mean-Field Glassy Systems
• Bosonic near-CFT${}_1$ models from Fock-space fluxes
• A dynamical version of the SYK Model and the q-Brownian Motion