Related papers: Percolation results for the Continuum Random Clust…
The appearance of the strongly interacting matter mixed phase (MP)has been suggested to consider to understand qualitatively the regime change existence in the behavior of some centrality depending characteristics of events. The MP has been…
The most studied continuum percolation model in two dimensions is the Boolean model consisting of disks with the same radius whose centers are randomly distributed on the Poisson point process (PPP). We also consider the Boolean percolation…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. If the phase transition of the model is second order, it can be equivalently described as a percolation transition of…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. We consider the the path-loss plus fading model of wireless signal…
We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We investigate the continuum q-Potts model at its transition point from the disordered to the ordered regime, with particular emphasis on the coexistence of disordered and ordered phases in the high-q case. We argue that occurrence of phase…
We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the…
In a statistical cluster or loop model such as percolation, or more generally the Potts models or O(n) models, a pinch point is a single bulk point where several distinct clusters or loops touch. In a polygon P harboring such a model in its…
An essential prerequisite for quark-gluon plasma production in nuclear collisions is cross-talk between the partons from different nucleons in the colliding nuclei. The initial density of partons is determined by the parton distribution…
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…
The phase-diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization group approximation. Our results suggest that, for any amount of randomness, the…
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we…
We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…