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.
- Block spin
- renormalization group
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics