Browsing by Subject "triangular lattice"

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    Exact Solution of the Classical Dimer Model on a Triangular Lattice: Monomer-Monomer Correlations
    (Springer, 2017-12) Basor, Estelle; Bleher, Pavel; Mathematical Sciences, School of Science
    We obtain an asymptotic formula, as n→∞, for the monomer–monomer correlation function K2(n) in the classical dimer model on a triangular lattice, with the horizontal and vertical weights wh=wv=1 and the diagonal weight wd=t>0, between two monomers at vertices q and r that are n spaces apart in adjacent rows. We find that tc=12 is a critical value of t. We prove that in the subcritical case, 0
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    The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice
    (Springer, 2018) Bleher, Pavel; Elwood, Brad; Petrović, Dražen; Mathematical Sciences, School of Science
    We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic matrices are all positive. The proof is based on the Kasteleyn identities and on small weight expansions. As an application, we obtain an asymptotic behavior of the dimer model partition function with an exponentially small error term.