Phase transitions in square-lattice dimer model with anisotropic interactions

A classical dimer model on a square lattice is studied. Anisotropic interactions between two neighboring dimers bring about phase transitions among a critical phase and columnar ordered phases. Based on a theoretical description and its similarity to that for a frustrated quantum spin chain, we shall point out an applicability of the level-spectroscopy method to locate the Berezinskii–Kosterlitz–Thouless transition points observed in the attractive case. We perform numerical transfer-matrix calculations to determine a global phase diagram, and also estimate the central charge in the critical phase. For the Gaussian transition between two-fold degenerate columnar phases, we check its universality via the finite-size-scaling analysis of excitation gaps.