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Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field

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UNSPECIFIED (2001) Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 289 (1-2). pp. 137-156.

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Abstract

The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution provided assumes the absence of external magnetic fields an extension to include a magnetic field along the z-axis is readily extracted. Furthermore, generalisations to a higher number of spin components on each site are possible within this method. We made numerical comparisons with the partition function from the earlier analytical expressions known in the literature for one- and two-dimensional cases. We find complete agreement with these studies. (C) 2001 Elsevier Science B.V. All rights reserved.

Item Type: Journal Article
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: 1 January 2001
Dates:
DateEvent
1 January 2001UNSPECIFIED
Volume: 289
Number: 1-2
Number of Pages: 20
Page Range: pp. 137-156
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

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