Abstract.
We prove that, just below the critical temperature, the mean field p-spins interaction model, for p suitably large, spontaneously decomposes into different states. The asymptotic overlaps between any two different states are zero. Under a mild (unproven) hypothesis on the weight distribution of these states, we prove that they are pure states. This situation is called in physics “one level of symmetry breaking”.
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Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000
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Talagrand, M. Rigorous low-temperature results for the mean field p-spins interaction model. Probab Theory Relat Fields 117, 303–360 (2000). https://doi.org/10.1007/s004400050009
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DOI: https://doi.org/10.1007/s004400050009