Replica theory and large-D Josephson junction hypercubic models

We study the statistical mechanics of a D-dimensional array of Josephson junctions in the 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 infinity . A conjectural form of the thermodynamic properties in the low-temperature phase is obtained by assuming that they are the same as 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.