Related papers: Crossover from percolation to diffusion
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
A previous scaling analysis of pressure experiments in heavy fermion is reviewed and enlarged. We show that the critical exponents obtained from this analysis indicate that a one-parameter scaling describes these experiments. We obtain…
Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…
We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \cite{Smirnov01criticalpercolation}, showing the existence of the universal and conformally invariant scaling limit of crossing…
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…
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
Explosive Percolation describes the abrupt onset of large-scale connectivity that results from a simple random process designed to delay the onset of the transition on an underlying random network or lattice. Explosive percolation…
The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
We investigate the description of current transfer in polycrystalline superconductors by percolation theory and its limitations. Various computer models that have been proposed are reviewed and related to the experimental and theoretical…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
It is shown that the universal critical properties of two recently introduced coupled directed percolation processes can be described by a single rapidity reversal invariant stochastic reaction-diffusion model. It is demonstrated that all…
Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomena in the coarse grained level, a…
In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special…