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arXiv · 0908.0120

Classical dimer model with anisotropic interactions on the square lattice

Hiromi Otsuka
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Abstract

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a two-fold ``zero-energy flat band'' in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.

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Hiromi Otsuka. 2009-08-02. Classical dimer model with anisotropic interactions on the square lattice. https://doi.org/10.1103/physreve.80.011140

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