Related papers: Explosive site percolation and finite size hystere…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
We study four Achlioptas type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entire holomorphic. The distributions of the order parameter, the…
A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
Mitra et al. [Phys. Rev. E 99 (2019) 012117] proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But the conclusion is…
The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections.…
Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also…
In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4th and the 5th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the…
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.…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…
Some examples of translation invariant site percolation processes on the $\Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given…