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Analytical expressions for energies, degeneracies and critical temperatures of the 2D square and 3D cubic Ising models
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UNSPECIFIED (2005) Analytical expressions for energies, degeneracies and critical temperatures of the 2D square and 3D cubic Ising models. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 349 (3-4). pp. 487-510. doi:10.1016/j.physa.2004.10.029 ISSN 0378-4371.
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Official URL: http://dx.doi.org/10.1016/j.physa.2004.10.029
Abstract
This paper revisits the fundamental statistical properties of the crucial model in critical phenomena i.e., the Ising model, guided by our knowledge of the energy values of the Ising Hamiltonian and aided by numerical estimation techniques. We have obtained exact energies in 2D and 3D and nearly exact analytical forms for the degeneracies of the distinct eigenvalues. The formulae we obtained, both for energies and degeneracies, have an exceedingly simple analytical form and are easy to use. The resultant partition functions were utilised to determine the critical behaviour of the Ising system on cubic lattices in 2D and 3D. We obtained a logarithmic divergence of the specific heat in the 2D case and the critical temperature estimates provided additional confirmation of the correctness of our approach. (C) 2004 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0378-4371 | ||||
Official Date: | 15 April 2005 | ||||
Dates: |
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Volume: | 349 | ||||
Number: | 3-4 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 487-510 | ||||
DOI: | 10.1016/j.physa.2004.10.029 | ||||
Publication Status: | Published |
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