Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-07-13
Phys. Rev. B 72, 144402 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
6 pages, 6 figures, journal reference added
Scientific paper
10.1103/PhysRevB.72.144402
The Ising spin-glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to investigate a recent conjecture which relates, on such pairs of dual lattices, the locations of the multicritical points, which occur on the Nishimori symmetry line. Towards this end we precisely determine the global phase diagrams for these six hierarchical spin-glasses, using up to 2.5 x 10^9 probability bins to represent the quenched distribution subjected to an exact renormalization-group transformation. We find in all three cases that the conjecture is realized to a very good approximation, even when the mutually dual models belong to different spatial dimensionalities d and have different phase diagram topologies at the multicritical points of the conjecture and even though the contributions to the conjecture from each lattice of the dual pair are strongly asymmetric. In all six phase diagrams, we find reentrance near the multicritical point. In the models with d=2 or 1.5, the spin-glass phase does not occur and the phase boundary between the ferromagnetic and paramagnetic phases is second order with a strong violation of universality. PACS numbers: 75.10.Nr, 64.60.Kw, 05.45.Df, 05.10.Cc
Berker Nihat A.
Hinczewski Michael
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