Classical dimers with aligning interactions on the square lattice

Abstract

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the non-interacting case of dimer coverings, including a Bethe Ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model and a free field analysis of height fluctuations.

26 pages, 32 figures, published version

References in corpus (5)

• Interacting classical dimers on the square lattice
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Unconventional continuous phase transition in a three dimensional dimer model
• Correlations and confinement in non-planar two-dimensional dimer models
• Doping quantum dimer models on the square lattice

Cited by in corpus (6)

• Coulomb gas transitions in three-dimensional classical dimer models
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Criticality of a classical dimer model on the triangular lattice
• Classical dimer model with anisotropic interactions on the square lattice
• Tetromino tilings and the Tutte polynomial
• Dimer Models, Free Fermions and Super Quantum Mechanics