Abstract
A spin glass problem on a Cayley tree with ferromagnetic interactions is solved rigorously. Using a level-I large deviation argument together with the martingale approach used by Buffet, Patrick and Pulé,(1) explicit expressions for the free energy are derived in different regions of the phase diagram. It is found that there are four phases: a paramagnetic phase, a spin-glass phase, a ferromagnetic phase and a mixed phase. The nature of the phase diagram depends on the power with which the ferromagnetic term occurs in the Hamiltonian.
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Wedagedera, J.R., Dorlas, T.C. The Phase Diagram of a Spin Glass Model. Journal of Statistical Physics 103, 697–716 (2001). https://doi.org/10.1023/A:1010340417836
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DOI: https://doi.org/10.1023/A:1010340417836