### Abstract

We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ^{2}) = (a/2)φ^{2} + Σ_{n = 2}^{M} {λ_{2n}/(2n)!} φ^{2n} (a real, λ_{2n} ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ_{4} take their mean-field values (i.e., γ = 1, α = 0, and Δ_{4} = 3/2).

Original language | English |
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Pages (from-to) | 2922-2929 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 26 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1985 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Hara, T., Hattori, T., & Tasaki, H. (1985). Skeleton inequalities and mean field properties for lattice spin systems.

*Journal of Mathematical Physics*,*26*(11), 2922-2929. https://doi.org/10.1063/1.526719