We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form a closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional percolation. In contrast to ...

Using a recently developed method to simulate percolation on large clusters of distributed machines [1], we have numerically calculated crossing, spanning and wrapping probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from Conformal Field Theory. We present many new results that await theoretical explanation, ...

A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path of least resi...

We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star–triangle transformation: We introduce a new parameter (the 3-body term) and identify configurations on the triangles solely by their connectivity. In this new setup, necessary and sufficient conditions are found for positive correlations and thi...

We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class...

A known result from marketing research is that many products fail to meet their expected market share. A possible explanation for this phenomenon is the inherent resistance of the social network, that is greatly increased if effects of negative word of mouth (NWOM) are taken into account. Here we suggest an extension for the Social Percolation framework that incorporates NWOM. The proposed mode...

Percolation problems have a wide range of applicability, and have therefore attracted a fair bit of attention over many years. Nevertheless the percolation thresholds, which are among the basic quantities for percolation on lattices, have been calculated exactly for only a few two-dimensional lattices. For many other lattices these thresholds have been calculated numerically. These numerical va...