Classical dimer model with anisotropic interactions on the square lattice

Details Classical dimer model with anisotropic interactions on the square lattice Classical dimer model with anisotropic interactions on the square lattice

2009-08-02

arxiv.org/abs/0908.0120v1

Phys. Rev. E 80, 011140 (2009)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 8 figures

Scientific paper

10.1103/PhysRevE.80.011140

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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