### Abstract

An asymptotically exact expression for the free energy of an (001) oriented domain wall of the 3D Ising model is derived. The order-disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. $J_x$ and $J_y$ ) are small compared to the third exchange energy ( $J_z$ ), the following equation for the critical temperature is derived, $\sinh\left(\frac{2J_z}{k_BT_c}\right)\sinh\left(\frac{2(J_x+J_y)}{k_BT_c}\right)=1.$ It is shown that this expression is asymptotically exact.

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 11 |

Publication status | Published - Mar 2007 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 2/1829 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- METIS-242078
- IR-67017
- EWI-9534

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## Cite this

Zandvliet, H. J. W., Saedi, A., & Hoede, C. (2007).

*The anisotropic 3D Ising model*. Enschede: University of Twente, Department of Applied Mathematics.