The m-component spin glass on a Bethe lattice

Abstract

We study the m-component vector spin glass in the limit m to infinity on a Bethe lattice. The cavity method allows for a solution of the model in a self-consistent field approximation and for a perturbative solution of the full problem near the phase transition. The low temperature phase of the model is analyzed numerically and a generalized Bose-Einstein condensation is found, as in the fully connected model. Scaling relations between four distinct zero-temperature exponents are found.

9 pages, 7 figures

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• Performance of a community detection algorithm based on semidefinite programming
• Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass