Lattices of effectively nonintegral dimensionality | Zendy

Deepak Dhar | Zendy

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Lattices of effectively nonintegral dimensionality

Author(s) -

Deepak Dhar

Publication year - 1977

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.523316

Subject(s) - curse of dimensionality , lattice (music) , tetrahedron , renormalization , statistical physics , mathematics , renormalization group , phase transition , physics , mathematical physics , condensed matter physics , geometry , statistics , acoustics

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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