The anisotropic 3D Ising model |
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| Authors: | H J W Zandvliet A Saedi C Hoede |
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| Institution: | 1. Physical Aspects of Nanoelectronics , MESA+ Institute for Nanotechnology, University of Twente , P. O. Box 217, 7500 AE Enschede, The Netherlands h.j.w.zandvliet@utwente.nl;3. Physical Aspects of Nanoelectronics , MESA+ Institute for Nanotechnology, University of Twente , P. O. Box 217, 7500 AE Enschede, The Netherlands;4. Department of Applied Mathematics , University of Twente , P. O. Box 217, 7500 AE Enschede, The Netherlands |
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| Abstract: | 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 /k B T c)sinh(2(Jx ?+?Jy )/k B T c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k B T c/Jz ?=?2ln(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. |
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| Keywords: | Phase transitions and critical phenomena Critical point effects Specific heats Short-range order |
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