Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-07-29
Journal Tech.Phys., v.36, 485 (1995)/partly/
Physics
Condensed Matter
Statistical Mechanics
22 pages, REVTEX
Scientific paper
In the paper nonlinear transformations of the Jordan-Wigner (JW) type are introduced in the form different from the ones known previously, for the purpose of expressing multi-index Pauli operators in terms of multi-index Fermi creation and annihilation operators. These JW transformations in the general case being a subject of a rather complicated algebra of transposition relations between various sets of Fermi creation and annihilation operators, depending on the common multiindex of the latter, is shown. As an example, the two- and three- dimensional transformations of the JW type are investigated, their properties and possible applications in analysis of a couple of lattice models of statistical mechanics and also an example of application of these transformations to problems of self-avoiding walks in graph theory, are discussed. The relation of the obtained transformations to the previously known transformations of the JW type for higher dimensions is shown.
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