### 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) |
---|---|

Pages (from-to) | 447-462 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 100 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1985 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

**Long range order in the anisotropic quantum ferromagnetic Heisenberg model.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 100, no. 3, pp. 447-462. https://doi.org/10.1007/BF01206139

}

TY - JOUR

T1 - Long range order in the anisotropic quantum ferromagnetic Heisenberg model

AU - Kennedy, Thomas G

PY - 1985/9

Y1 - 1985/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041083368&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041083368&partnerID=8YFLogxK

U2 - 10.1007/BF01206139

DO - 10.1007/BF01206139

M3 - Article

AN - SCOPUS:0041083368

VL - 100

SP - 447

EP - 462

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -