Classical dimers on the triangular lattice

P. Fendley, R. Moessner, Shivaji Lal Sondhi

Research output: Contribution to journalArticle

97 Scopus citations

Abstract

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble using Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value 0.1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes noncritical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square lattice problem.

Original languageEnglish (US)
Article number214513
Pages (from-to)2145131-21451314
Number of pages19306184
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume66
Issue number21
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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