## Abstract

We study the four-dimensional n-component | φ| ^{4} spin model for all integers n≥ 1 and the four-dimensional continuous-time weakly self-avoiding walk which corresponds exactly to the case n= 0 interpreted as a supersymmetric spin model. For these models, we analyse the correlation length of order p, and prove the existence of a logarithmic correction to mean-field scaling, with power 12n+2n+8, for all n≥ 0 and p> 0. The proof is based on an improvement of a rigorous renormalisation group method developed previously.

Original language | English (US) |
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Pages (from-to) | 375-402 |

Number of pages | 28 |

Journal | Annales Henri Poincare |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2017 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics

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