Spin-glass behaviour on random lattices. (English) Zbl 1456.82914
Summary: The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction \(w\) of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that \(w = 1/2\), corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase \((w < 1/2)\) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases \((w > 1/2)\).
MSC:
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
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