Doping quantum dimer models on the square lattice

Doping quantum dimer models on the square lattice

Antiferromagnetic Potts models on the square lattice.

We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Koteck y Monte Carlo algorithm and a new nite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length 5000; the data are consistent with () = Ae 2 (1 + a 1 e +. . .) as ! 1. For q = 4 the model is disordered even at zero temperature.

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 "...

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...

Complex-temperature singularities in Potts models on the square lattice.

We report some results on the complex-temperature ~CT! singularities of q-state Potts models on the square lattice. We concentrate on the problematic region Re(a),0 ~where a5e) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for 3<q<8, we establish the existence, in this region, of complex-conjugate CT sin...