Abstract
We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.
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Carlson, J.M., Chayes, J.T., Chayes, L. et al. Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis. J Stat Phys 61, 987–1067 (1990). https://doi.org/10.1007/BF01014364
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DOI: https://doi.org/10.1007/BF01014364