# The anisotropic 3D Ising model

Henricus J.W. Zandvliet, A. Saedi, C. Hoede

Research output: Book/ReportReportProfessional

6 Citations (Scopus)

### 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 Enschede University of Twente, Department of Applied Mathematics 11 Published - Mar 2007

### Publication series

Name Department of Applied Mathematics, University of Twente 2/1829 1874-4850 1874-4850

• METIS-242078
• IR-67017
• EWI-9534

• ## Cite this

Zandvliet, H. J. W., Saedi, A., & Hoede, C. (2007). The anisotropic 3D Ising model. Enschede: University of Twente, Department of Applied Mathematics.