Ising spin glasses on Wheatstone-Bridge hierarchical lattices

Abstract Nearest-neighbor-interaction Ising spin glasses are studied on three different hierarchical lattices, all of them belonging to the Wheatstone–Bridge family. It is shown that the spin glass lower critical dimension in these lattices should be greater than 2.32. Finite-temperature spin glass phases are found for a lattice of fractal dimension D ≈ 3.58 (whose unit cell is obtained from a simple construction of a part of the cubic lattice), as well as for a lattice of fractal dimension close to five. In the former case, the estimates of spin glass critical temperatures associated with symmetric Gaussian and bimodal distributions are very close to recent results from extensive numerical simulations carried on a cubic lattice, suggesting that whole phase diagrams presented, obtained for couplings following non-centered distributions – not known up to the moment for Bravais lattices – should represent good approximations.