Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis |
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| Authors: | J M Carlson J T Chayes L Chayes J P Sethna D J Thouless |
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| Institution: | (1) Institute for Theoretical Physics, University of California, 93106 Santa Barbara, California;(2) Department of Mathematics, University of California, 90024 Los Angeles, California;(3) Department of Physics, Cornell University, 14853 Ithaca, New York;(4) Department of Physics, University of Washington, 98195 Seattle, Washington |
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| 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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| Keywords: | Spin glass Bethe lattice bifurcation critical phenomena |
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