Replica Theory and Large D Josephson Junction Hypercubic Models

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.

latex 35 pages, including figures added in uufiles format

References in corpus (5)

• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation
• Self Induced Quenched Disorder: A Model for the Glass Transition
• $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators
• The Fully Frustrated Hypercubic Model is Glassy and Aging at Large $D$

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• How to realize compact and non-compact localized states in disorder-free hypercube networks
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• Classical and Quantum Behavior in Mean-Field Glassy Systems