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Lattices of effectively nonintegral dimensionality

Dhar, Deepak (1977) Lattices of effectively nonintegral dimensionality. Journal of Mathematical Physics, 18 (4). pp. 577-585. ISSN 0022-2488. doi:10.1063/1.523316.

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We construct a class of lattice systems that have effectively nonintegral dimensionality. A reasonable definition of effective dimensionality applicable to lattice systems is proposed and the effective dimensionalities of these lattices are determined. The renormalization procedure is used to determine the critical behavior of the classical XY model and the Fortuin–Kasteleyn cluster model on the truncated tetrahedron lattice which is shown to have the effective dimensionality 2 log3 /log5. It is found that no phase transition occurs at any finite temperature.

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Additional Information:© 1977 American Institute of Physics. Received 2 September 1976. I am deeply indebted to my advisor, Professor Jon Mathews, for his encouragement, discussions, and critical comments throughout the course of this investigation. The financial support of the H. Dudley Wright Foundation is gratefully acknowledged.
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H. Dudley Wright FoundationUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 05.50.+q
Record Number:CaltechAUTHORS:20120806-140745851
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32953
Deposited By: Tony Diaz
Deposited On:06 Aug 2012 21:47
Last Modified:09 Nov 2021 21:31

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