### Abstract

Let S_{n} 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 S_{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)/n^{1-1/2k} has a limiting distribution with density proportional to exp[-λ_{s}^{2k}/(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 1 1978 |

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### Keywords

- Block spin
- Curie-Weiss
- mean-field
- renormalization group

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*19*(2), 149-161. https://doi.org/10.1007/BF01012508