Critical behavior of a three-dimensional dimer model

Bhattacharjee, Somendra M. ; Nagle, John F. ; Huse, David A. ; Fisher, Michael E. (1983) Critical behavior of a three-dimensional dimer model Journal of Statistical Physics, 32 (2). pp. 361-374. ISSN 0022-4715

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The phase transition behavior of a dimer model on a three-dimensional lattice is studied. This model is of biological interest because of its relevance to the lipid bilayer main phase transition. The model has the same kind of inactive low-temperature behavior as the exactly solvable Kasteleyn dimer model on a two-dimensional honeycomb lattice. Because of low-temperature inactivity, determination of the lowest-lying excited states allows one to locate the critical temperature. In this paper the second-lowest-lying excited states are studied and exact asymptotic results are obtained in the limit of large lattices. These results together with a finite-size scaling ansatz suggest a logarithmic divergence of the specific heat aboveT c for the three-dimensional model. Use of the same ansatz recovers the exact divergence (α=½) for the two-dimensional model.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Dimer Model; Phase Transition; Lipid Bilayer; Transfer Matrix; Random Walk; Generating Function; Critical Exponent
ID Code:2957
Deposited On:09 Oct 2010 10:28
Last Modified:16 May 2016 13:50

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