Related papers: Universality of percolation at dynamic pseudocriti…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
In this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension. In particular we determine numerically the order parameter, its fluctuations as well as the susceptibility as a function…
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…
We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…
We consider the growth of clusters in disordered media at zero temperature, as exemplified by supercritical generalized percolation and by the random field Ising model. We show that the morphology of such clusters and of their surfaces can…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…
Universal scaling near phase transitions is one of the central ideas of physics, linking the growth of spatial correlations to the slowing down of dynamics. So far, direct experimental access to this critical behavior has remained largely…
We investigate site percolation on a weighted planar stochastic lattice (WPSL) which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by percolation threshold $p_c$ and by a set of critical…
We find that 2-dimensional (2-D) critical branched polymers with no impurities conclusively belong to the same universality class as 2-D random percolation clusters, although pure critical 3-D branched polymers do not belong to the 3-D…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular $d$-dimensional hypercubic lattices are in the present work investigated using the…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…