# 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 Undefined 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.
Zandvliet, Henricus J.W. ; Saedi, A. ; Hoede, C. / The anisotropic 3D Ising model. Enschede : University of Twente, Department of Applied Mathematics, 2007. 11 p.
title = "The anisotropic 3D Ising model",
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.",
keywords = "METIS-242078, IR-67017, EWI-9534",
author = "Zandvliet, {Henricus J.W.} and A. Saedi and C. Hoede",
year = "2007",
month = "3",
language = "Undefined",
publisher = "University of Twente, Department of Applied Mathematics",
number = "2/1829",

}

Zandvliet, HJW, Saedi, A & Hoede, C 2007, 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.

Enschede : University of Twente, Department of Applied Mathematics, 2007. 11 p.

Research output: Book/ReportReportProfessional

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 -

Zandvliet HJW, Saedi A, Hoede C. The anisotropic 3D Ising model. Enschede: University of Twente, Department of Applied Mathematics, 2007. 11 p.