New percolation structures in dilute antiferromagnetic Potts models.

Abstract

We introduce a new class of site-percolation models and study them by Monte Carlo methods. These percolation models are defined as the zero-temperature limit of a quench-diluted spin model whose symmetries are those of the antiferromagnetic three-state Potts model on a triangular lattice. Many of these percolation models exhibit a sequence of two percolation transitions. A new phase, excluded in the absence of dilution, is found at intermediate spin concentrations. This phase, which we call the chiral phase, exhibits the symmetries of only a subgroup of the full symmetry group of the Potts model. The critical properties of the transitions found in these percolation models have been studied. The results indicate that, for this entire class of percolation models, the observed transitions are all contained in the universality class of the geometric percolation (q=1 Potts) model. From this result we conclude that the breaking of symmetry, which is relevant for thermally driven transitions, is not relevant for percolation transitions.