Related papers: Crossover from Isotropic to Directed Percolation
We study the absorbing phase transitions in coupled directed percolation (DP) processes with $N$-species particles in one dimension. The interspecies coupling is linear, bidirectional, and excitatory. We find that the presence of a…
We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This…
We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…
In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward $\epsilon$-movability which will be a key tool for our analysis.
Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive…
The culling process in Bootstrap Percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap…
The study presented here addresses the challenging problem of laminar-turbulent flow transition in boundary layers. Directed percolation theory has emerged as a promising approach to understand and describe this transition in different…
For thermal transport in one-dimensional (1D) systems, recent studies have suggested that employing different theoretical models and different numerical simulations under different system's parameter regimes might lead to different…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
Consider percolation on $T\times \mathbb{Z}^d$, the product of a regular tree of degree $k\geq 3$ with the hypercubic lattice $\mathbb{Z}^d$. It is known that this graph has $0<p_c<p_u<1$, so that there are non-trivial regimes in which…
We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…
We generate point configurations (PCs) by thresholding the local energy of the Ashkin-Teller model in two dimensions (2D) and study the percolation transition at different values of $\lambda$ along the critical Baxter line by varying the…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We…
Correlations between electrical and thermal conduction in polymer composites are blurred due to the complex contribution of charge and heat carriers at the nanoscale junctions of filler particles. Conflicting reports on the lack or…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
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…