### Abstract

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin -1/2 Ising models, φ{symbol}^{4} field theories, and other continuous spin models. The proofs are based on the properties of a class G^{-} of probability measures which contains all measures of the form const exp(-V(x))dx, where V is even and continuously differentiable and dV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.

Original language | English (US) |
---|---|

Pages (from-to) | 167-182 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1976 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*46*(2), 167-182. https://doi.org/10.1007/BF01608495

**The GHS and other correlation inequalities for a class of even ferromagnets.** / Ellis, Richard S.; Monroe, James L.; Newman, Charles M.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 46, no. 2, pp. 167-182. https://doi.org/10.1007/BF01608495

}

TY - JOUR

T1 - The GHS and other correlation inequalities for a class of even ferromagnets

AU - Ellis, Richard S.

AU - Monroe, James L.

AU - Newman, Charles M.

PY - 1976/6

Y1 - 1976/6

N2 - We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin -1/2 Ising models, φ{symbol}4 field theories, and other continuous spin models. The proofs are based on the properties of a class G- of probability measures which contains all measures of the form const exp(-V(x))dx, where V is even and continuously differentiable and dV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.

AB - We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin -1/2 Ising models, φ{symbol}4 field theories, and other continuous spin models. The proofs are based on the properties of a class G- of probability measures which contains all measures of the form const exp(-V(x))dx, where V is even and continuously differentiable and dV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.

UR - http://www.scopus.com/inward/record.url?scp=0000868919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000868919&partnerID=8YFLogxK

U2 - 10.1007/BF01608495

DO - 10.1007/BF01608495

M3 - Article

VL - 46

SP - 167

EP - 182

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -