### Abstract

We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic φ{symbol}^{4} lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2 n-point functions are also given. A simple construction of the continuum φ{symbol}_{d}
^{4} quantum field theory (d<4), based on these inequalities, is described in a companion paper.

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

Pages (from-to) | 117-139 |

Number of pages | 23 |

Journal | Communications in Mathematical Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1983 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*91*(1), 117-139. https://doi.org/10.1007/BF01206055

**The random-walk representation of classical spin systems and correlation inequalities - II. The skeleton inequalities.** / Brydges, David C.; Fröhlich, Jürg; Sokal, Alan D.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 91, no. 1, pp. 117-139. https://doi.org/10.1007/BF01206055

}

TY - JOUR

T1 - The random-walk representation of classical spin systems and correlation inequalities - II. The skeleton inequalities

AU - Brydges, David C.

AU - Fröhlich, Jürg

AU - Sokal, Alan D.

PY - 1983/3

Y1 - 1983/3

N2 - We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic φ{symbol}4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2 n-point functions are also given. A simple construction of the continuum φ{symbol}d 4 quantum field theory (d<4), based on these inequalities, is described in a companion paper.

AB - We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic φ{symbol}4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2 n-point functions are also given. A simple construction of the continuum φ{symbol}d 4 quantum field theory (d<4), based on these inequalities, is described in a companion paper.

UR - http://www.scopus.com/inward/record.url?scp=33749316706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749316706&partnerID=8YFLogxK

U2 - 10.1007/BF01206055

DO - 10.1007/BF01206055

M3 - Article

AN - SCOPUS:33749316706

VL - 91

SP - 117

EP - 139

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -