Ising Spin Glasses on Wheatstone-Bridge Hierarchical Lattices Octavio R. Salmon 1 , $^{2}$, ∗ Br´ aulio T. Agostini $^{1}$, † and Fernando D. Nobre 1 , 2 ‡ $^{1}$Centro Brasileiro de Pesquisas F´ısicas Rua Xavier Sigaud 150 22290-180 Rio de Janeiro - RJ Brazil $^{2}$National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150 22290-180 Rio de Janeiro - RJ Brazil (Dated: November 2, 2018) Nearest-neighbor-interaction Ising spin glasses are studied on three different hierar- chical 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 dimen- sion 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 for- mer case, the estimates of spin-glass critical temperatures associated with symmetric Gaussian and bimodal distributions are very close to recent results from extensive nu- merical 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. Keywords: Spin Glasses, Hierarchical Lattices, Phase Diagrams. PACS numbers: 75.10.Nr, 05.50.+q, 75.50.Lk, 64.60.-i $^{∗}$E-mail address: octavior@cbpf.br $^{†}$E-mail address: agostini@cbpf.br $^{‡}$Corresponding author: E-mail address: fdnobre@cbpf.br; FAX: 55-21-21417401; arXiv:1002.2026v1 [cond-mat.stat-mech] 10 Feb 2010 Abstract