Interacting double dimer model on the square lattice

Quantum model of interacting “ strings ” on the square lattice

Quantum model of interacting " strings " on the square lattice Abstract The model which is the generalization of the one-dimensional XY-spin chain for the case of the two-dimensional square lattice is considered. The subspace of the " string " states is studied. The solution to the eigenvalue problem is obtained for the single " string " in cases of the " string " with fixed ends and " string "...

Interacting classical dimers on the square lattice.

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separati...

Phase transitions in square-lattice dimer model with anisotropic interactions

In the early 1960s, Kasteleyn [1] and Temperley and Fisher [2] discussed the statistical mechanics for covering problem of graphs by dimers. In particular, the close-packed dimer models on planar graphs were revealed to be solved by Pfaffian method, so they have been recognized to be in a exactly solvable class. While dimers have obvious relevance to diatomic molecules adsorbed on surfaces, the...

Doping quantum dimer models on the square lattice

Semi-flexible interacting self-avoiding trails on the square lattice

Self-avoiding walks self-interacting via nearest neighbours (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the polymer collapse transition of a polymer in a dilute solution. On the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class. It has been shown that by adding ...