### 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) |
---|---|

Pages (from-to) | 149-161 |

Number of pages | 13 |

Journal | Journal of Statistical Physics |

Volume | 19 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1978 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**The statistics of Curie-Weiss models.** / Ellis, Richard S.; Newman, Charles M.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 19, no. 2, pp. 149-161. https://doi.org/10.1007/BF01012508

}

TY - JOUR

T1 - The statistics of Curie-Weiss models

AU - Ellis, Richard S.

AU - Newman, Charles M.

PY - 1978/8

Y1 - 1978/8

N2 - 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[-λs 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.

AB - 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[-λs 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.

KW - Block spin

KW - Curie-Weiss

KW - mean-field

KW - renormalization group

UR - http://www.scopus.com/inward/record.url?scp=0009004363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009004363&partnerID=8YFLogxK

U2 - 10.1007/BF01012508

DO - 10.1007/BF01012508

M3 - Article

VL - 19

SP - 149

EP - 161

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -