dc.creator | Bauerschmidt, Roland | |

dc.creator | Slade, G | |

dc.creator | Wallace, BC | |

dc.date.accessioned | 2017-01-09 | |

dc.date.accessioned | 2018-11-24T23:27:05Z | |

dc.date.available | 2017-03-24T10:31:35Z | |

dc.date.available | 2018-11-24T23:27:05Z | |

dc.date.issued | 2017-04-01 | |

dc.identifier | https://www.repository.cam.ac.uk/handle/1810/263207 | |

dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3941 | |

dc.description.abstract | We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}$$^{4}$, for sufficiently small attraction. We prove that the susceptibility and correlation length of order $\textit{p}$ (for any $\textit{p}$ > 0) have logarithmic corrections to mean field scaling, and that the critical two-point function is asymptotic to a multiple of |x|$^{-2}$. This shows that small contact self-attraction results in the same critical behaviour as no contact self-attraction; a collapse transition is predicted for larger self-attraction. The proof uses a supersymmetric representation of the two-point function, and is based on a rigorous renormalisation group method that has been used to prove the same results for the weakly self-avoiding walk, without self-attraction. | |

dc.language | en | |

dc.publisher | Springer | |

dc.publisher | Journal of Statistical Physics | |

dc.subject | weakly self-avoiding walk | |

dc.subject | collapse transition | |

dc.subject | renormalisation group | |

dc.title | Four-Dimensional Weakly Self-avoiding Walk with Contact Self-attraction | |

dc.type | Article | |