Related papers: Recent advances in percolation theory and its appl…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…
A simple non-interacting-electron model, combining local quantum tunneling and global classical percolation (due to a finite dephasing time at low temperatures), is introduced to describe a metal-insulator transition in two dimensions. It…
$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural…
Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…