Related papers: Percolation-like phase transition in a non-equilib…
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree…
We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the model is supercritical:…
We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…
In rotationally constrained percolation models, a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint. A state variable $s_i$ is assigned to each lattice…
The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe…
We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangular sample using Ginzburg-Landau (GL) and quasi-classical (QC) Green's function theory. Except for a square sample with parameters far away…
The ground-state of an infinite-range Potts glass-type model with +/- J bonds and unrestricted number of states is used to investigate coalition formation. As a function of the q probability of +J bonds in the system it is found that the r…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
We study oriented percolation on random causal triangulations, those are random planar graphs obtained roughly speaking by adding horizontal connections between vertices of an infinite tree. When the underlying tree is a geometric…
We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites.…
A class of proposed coherent precipitate structures (Guinier-Preston zones) in the Al-Mg-Si alloy are investigated using first-principles density functional theory methods. The cluster expansion method is used to extract effective…
Given a quasi-transitive infinite graph $G$ with volume growth rate ${\rm gr}(G),$ a transient biased electric network $(G,\, c_1)$ with bias $\lambda_1\in (0,\,{\rm gr}(G))$ and a recurrent biased one $(G,\, c_2)$ with bias $\lambda_2\in…
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric…
We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erd\H{o}s--R\'enyi graph to a $2D$ lattice at the characteristic interaction…
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…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
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…