Spin and magnetism
Subtitle: two transfer matriz formulations of a classical Heisenberg Ring in a Magnetic Field
By: Randall J. Franciose
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1998
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 53
Description: Nanometer scale fabrication and experimental investigations into the magnetic properties of mesoscopic      molecular clusters have specifically addressed the need for theoretical models to as certain thermodynamic      properties. Technological applications germane to these inquiries potentially include minimum scale      ferromagnetic data storage and quantum computing. The one- dimensional nearest neighbor Heisenberg spin      system accurately models the energy exchange of certain planar rings of magnetic ions. Seeking the partition      function from which a host of thermodynamic quantities may be obtained, this thesis contrasts two transfer      matrix formulations of a classical Heisenberg ring in a magnetic field. Following a discussion of the transfer      matrix technique in an Ising model and a review of material magnetic characteristics, a Heisenberg Hamiltonian      development establishes the salient integral eigenvalue equation. The 1975 technique of Blume et al turns the      integral equation into a matrix eigenvalue equation using Gaussian numerical integration. This thesis alternatively      proposes an exactly formulated matrix eigenvalue equation, deriving the matrix elements by expanding the      eigenvectors in a basis of the spherical harmonics. Representing the energy coupling of the ring to a magnetic      field with symmetric or asymmetric transfer operators develops pragmatically distinctive matrix elements; the      asymmetric yielding a simpler expression. Complete evaluation will require follow-on numerical analysis.
Notes: Thesis advisor(s): James H. Luscombe.

"June 1998."

Thesis (M.S. in Physics) Naval Postgraduate School, June 1998.

Includes bibliographical references (p. 51-52).

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US Navy (USN) author.

dk/dk cc:9116 9/2/98.