Criticality of a classical dimer model on the triangular lattice.

We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short-range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition to an ordered columnar phase for large interactions. Our results indicate that criticality and nonbipartiteness are compatible in a dimer model. For the isotropic triangular case, we have indications that the system undergoes a first-order phase transition to an ordered phase, without appearance of an intermediate critical phase.

Gauge theory picture of an ordering transition in a dimer model.

We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3D XY model. The continuous nature of the transition is confirmed by a flowgram analysis.

Spin gap and string order parameter in the ferromagnetic spiral staircase heisenberg ladder: a quantum Monte Carlo study.

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J perpendicular and inequivalent chains. This model is obtained by a twist (theta) deformation of the ladder and interpolates between the isotropic ladder (theta=0) and the SU(2) ferromagnetic Kondo necklace model (theta = pi). We show that the ground state in the (theta, J perpendicular) plane has a finite string order parameter characterizing the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from delta/J parallel proportional, variant J perpendicular/J parallel for theta < theta c approximately 8 pi/9 to delta/J parallel proportional, variant (J perpendicular/J parallel)2 for theta > theta c. Those results are obtained on the basis of large scale quantum Monte Carlo calculations.

Néel temperature of quasi-low-dimensional Heisenberg antiferromagnets.

The Néel temperature T(N) of quasi-one- and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of interchain (interlayer) to intrachain (intralayer) coupling J(')/J down to J(')/J approximately = 10(-3). We find that T(N) obeys a modified random-phase approximationlike relation for small J(')/J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulas describing T(N) for a wide range of J(') and useful for the analysis of experimental measurements are presented.