### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 11 |

Publication status | Published - Mar 2007 |

### Publication series

Name | |
---|---|

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

### Cite this

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

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

**The anisotropic 3D Ising model.** / Zandvliet, Henricus J.W.; Saedi, A.; Hoede, C.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - The anisotropic 3D Ising model

AU - Zandvliet, Henricus J.W.

AU - Saedi, A.

AU - Hoede, C.

PY - 2007/3

Y1 - 2007/3

N2 - 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.

AB - 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.

KW - METIS-242078

KW - IR-67017

KW - EWI-9534

M3 - Report

BT - The anisotropic 3D Ising model

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -