Abstract
Let Sn denote the random total magnetization of an n-site Curie-Weiss model, a collection of n (spin) random variables with an equal interaction of strength 1/n between each pair of spins. The asymptotic behavior for large n of the probability distribution of Sn 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 (Sn-nm)/n1-1/2k has a limiting distribution with density proportional to exp[-λs2k/(2k)!], where m 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.
Original language | English (US) |
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Pages (from-to) | 149-161 |
Number of pages | 13 |
Journal | Journal of Statistical Physics |
Volume | 19 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1978 |
Keywords
- Block spin
- Curie-Weiss
- mean-field
- renormalization group
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics