Classical dimer model with anisotropic interactions on the square lattice

TL;DR

This paper investigates the phase transitions and phase diagram of a classical anisotropic dimer model on a square lattice, revealing Berezinskii-Kosterlitz-Thouless transitions and phase boundaries through numerical and theoretical analysis.

Contribution

It introduces criteria for transition points and universal level-splitting conditions, applying them to determine the phase diagram of the anisotropic dimer model.

Findings

Identification of BKT transitions from dimer-liquid to columnar phases

Determination of phase boundaries between dimer-liquid and strong repulsion phases

Analysis of the flat band in the strong repulsion limit

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.