Abstract
LetS n denote the random total magnetization of ann-site Curie-Weiss model, a collection ofn (spin) random variables with an equal interaction of strength 1/n between each pair of spins. The asymptotic behavior for largen of the probability distribution ofS n is analyzed and related to the well-known (mean-field) thermodynamic properties of these models. One particular result is that at a type-k critical point (S n-nm)/n1−1/2k has a limiting distribution with density proportional to exp[-λs 2k/(2k)!], wherem is the mean magnetization per site and A is a positive critical parameter with a universal upper bound. Another result describes the asymptotic behavior relevant to metastability.
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Research supported in part by National Science Foundation Grants MPS 76-06644 (to RSE) and MPS 74-04870 A01 (to CMN).
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Ellis, R.S., Newman, C.M. The statistics of Curie-Weiss models. J Stat Phys 19, 149–161 (1978). https://doi.org/10.1007/BF01012508
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DOI: https://doi.org/10.1007/BF01012508