Loop Model with Generalized Fugacity in Three Dimensions

Details Loop Model with Generalized Fugacity in Three Dimensions Loop Model with Generalized Fugacity in Three Dimensions

1999-07-22

arxiv.org/abs/cond-mat/9907335v4

J.Phys.A33:1661-1673,2000

Physics

Condensed Matter

Statistical Mechanics

16pages, 4 eps figures, (v2) typos and Table 3 corrected. Refs added, (v3) an error in an explanation of fig.2 corrected. Refs

Scientific paper

10.1088/0305-4470/33/8/310

A statistical model of loops on the three-dimensional lattice is proposed and is investigated. It is O(n)-type but has loop fugacity that depends on global three-dimensional shapes of loops in a particular fashion. It is shown that, despite this non-locality and the dimensionality, a layer-to-layer transfer matrix can be constructed as a product of local vertex weights for infinitely many points in the parameter space. Using this transfer matrix, the site entropy is estimated numerically in the fully packed limit.

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