Rigorous low-temperature results for the mean field p-spins interaction model |
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| Authors: | Michel Talagrand |
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| Affiliation: | (1) Equipe d'Analyse Tour 46, ESA au CNRS no. 7064, Université Paris VI, 4 Jussieu, 75230 Paris Cedex 05, France (e-mail: mit@ccr.jussieu.fr), FR;(2) Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA. e-mail: talagran@math.ohio-state.edu, US |
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| 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”. Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000 |
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| Keywords: | Mathematics Subject Classification (2000): Primary 82A87 Secondary 66G15, 60E15 |
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