We simulate the bond and site percolation models on several three-dimensional lattices,
including the diamond, body-centered cubic, and face-centered cubic lattices. As on the …

The critical curves of the q-state Potts model can be determined exactly for regular two-
dimensional lattices G that are of the three-terminal type. This comprises the square …

We propose a simple percolation criterion for arbitrary percolation problems. The basic idea
is to decompose the system of interest into a hierarchy of neighborhoods, such that the …

We present a rough estimation—up to four significant digits, based on the scaling hypothesis
and the probability of belonging to the largest cluster vs the occupation probability—of the …

Percolation thresholds have recently been studied by means of a graph polynomial PB (p),
henceforth referred to as the critical polynomial, that may be defined on any periodic lattice …

The percolation behavior of composites comprising complex-shaped particles is a recurrent
problem in materials science. Previous studies focused on the symmetric particles such as …

We show analytically that the [0, 1],[1, 1], and [2, 1] Padé approximants of the mean cluster
number S (p) for site and bond percolation on general d-dimensional lattices are upper …

We give a conditional derivation of the inhomogeneous critical percolation manifold of the
bow-tie lattice with five different probabilities, a problem that does not appear at first to fall …

In our previous work [1] we have shown that critical manifolds of the q-state Potts model can
be studied by means of a graph polynomial PB (q, v), henceforth referred to as the critical …

Any two-dimensional infinite regular lattice G can be produced by tiling the plane with a finite
subgraph B⊆ G; we call B a basis of G. We introduce a two-parameter graph polynomial PB …