The anisotropic 3D Ising model

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

Research output: Book/ReportReportProfessional

6 Citations (Scopus)
67 Downloads (Pure)

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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages11
Publication statusPublished - Mar 2007

Publication series

Name
PublisherDepartment 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

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.
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author = "Zandvliet, {Henricus J.W.} and A. Saedi and C. Hoede",
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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.