Related papers: Two Types of Discontinuous Percolation Transitions…
Percolation transition (PT) means the formation of a macroscopic-scale large cluster, which exhibits a continuous transition. However, when the growth of large clusters is globally suppressed, the type of PT is changed to a discontinuous…
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 internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
Discontinuous transition is observed in the equilibrium cluster properties of a percolation model with suppressed cluster growth as the growth parameter g0 is tuned to the critical threshold at sufficiently low initial seed concentration…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
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…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Glass-like materials are nonequilibrium systems where the relaxation time may exceed reasonable time scales of observations. In the present paper a dynamic percolation model is introduced in order to explain the principal properties of…
Monte Carlo computer simulations of a quasi two dimensional (2D) dipolar fluid at low and intermediate densities indicate that the structure of the fluid is well described by an ideal mixture of self-assembling clusters. A detailed analysis…
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 the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…