### Abstract

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

Pages (from-to) | 981-986 |

Number of pages | 6 |

Journal | Phase transitions |

Volume | 80 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- METIS-242115
- IR-73058

### Cite this

*Phase transitions*,

*80*(9), 981-986. https://doi.org/10.1080/01411590701462708

}

*Phase transitions*, vol. 80, no. 9, pp. 981-986. https://doi.org/10.1080/01411590701462708

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

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - The Anisotropic 3D Ising model

AU - Zandvliet, Henricus J.W.

AU - Saedi, A.

AU - Hoede, C.

PY - 2007

Y1 - 2007

N2 - An expression for the free energy of an (001) oriented domain wall of the anisotropic 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. Jx and Jy) are small compared to the third exchange energy (Jz), the following asymptotically exact equation for the critical temperature is derived, sinh(2Jz/kBTc)sinh(2(Jx + Jy)/kBTc)) = 1. This expression is in perfect agreement with a mathematically rigorous result (kBTc/Jz = 2[ln(Jz/(Jx + Jy))-ln(ln(Jz/(Jx + Jy)) + O(1)]-1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ∼0.84 at ((Hx + Hy)/Hz) = 10-2 to ∼0.76 at ((Hx + Hy)/Hz) = 10-20.

AB - An expression for the free energy of an (001) oriented domain wall of the anisotropic 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. Jx and Jy) are small compared to the third exchange energy (Jz), the following asymptotically exact equation for the critical temperature is derived, sinh(2Jz/kBTc)sinh(2(Jx + Jy)/kBTc)) = 1. This expression is in perfect agreement with a mathematically rigorous result (kBTc/Jz = 2[ln(Jz/(Jx + Jy))-ln(ln(Jz/(Jx + Jy)) + O(1)]-1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ∼0.84 at ((Hx + Hy)/Hz) = 10-2 to ∼0.76 at ((Hx + Hy)/Hz) = 10-20.

KW - METIS-242115

KW - IR-73058

U2 - 10.1080/01411590701462708

DO - 10.1080/01411590701462708

M3 - Article

VL - 80

SP - 981

EP - 986

JO - Phase transitions

JF - Phase transitions

SN - 0141-1594

IS - 9

ER -