### Abstract

We study the anisotropic quantum mechanical ferromagnetic Heisenberg model. By anisotropic we mean that the x and y exchange constants are equal but smaller than the z exchange constant. We show that for any amount of anisotropy there is long range order in two or more dimensions at low enough temperature. We also develop a convergent low temperature expansion and use it to prove exponential decay of the truncated correlation functions.

Original language | English (US) |
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Pages (from-to) | 447-462 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 100 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1985 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics