Critical behavior of a three-dimensional dimer model

Somendra M. Bhattacharjee, John F. Nagle, David A. Huse, Michael E. Fisher

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45 Scopus citations

Abstract

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 above Tc for the three-dimensional model. Use of the same ansatz recovers the exact divergence (α=1/2) for the two-dimensional model.

Original languageEnglish (US)
Pages (from-to)361-374
Number of pages14
JournalJournal of Statistical Physics
Volume32
Issue number2
DOIs
StatePublished - Aug 1 1983
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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