### Abstract

A simple route to determine the boundary tension of Ising models is proposed. As pointed out by Onsager, the boundary tension is an important quantity since it vanishes at the critical temperature and can thus be used to determine the critical temperature. Here we derive expressions for the boundary tension along various high symmetry directions of the anisotropic square and triangular lattices. The exact results by respectively Onsager (Phys. Rev. 65, 117 (1944)) for the anisotropic square lattice and by Houtappel (Physica 16, 435 (1950)) for the anisotropic triangular lattice are reproduced. Subsequently, we will apply our method to Ising models that have not been exactly solved yet. Valuable results are obtained for the 2D square Ising lattice with nearest and weak next��?nearest neighbour interactions as well as for the strongly anisotropic 3D Ising lattice.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 24 |

Publication status | Published - Sep 2008 |

### Publication series

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

No. | Supplement/1880 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- EWI-13393
- PACS-64.60.-i
- PACS-64.60.De
- IR-64962
- METIS-251159

## Cite this

Zandvliet, H. J. W., & Hoede, C. (2008).

*Boundary tension of 2D and 3D Ising models*. Enschede: University of Twente, Department of Applied Mathematics.