Related papers: Percolation transitions with nonlocal constraint
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…
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…
Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However,…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
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…
We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
We investigate a novel variant of the exclusion process in which particles perform asymmetric nearest-neighbor jumps across a bond \((k, k+1)\) only if the preceding site \((k-1)\) is unoccupied. This next-nearest-neighbor constraint…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
In this paper we characterize the superconductor-insulator phase transition on a network of 2d percolation clusters. Sufficiently close to the percolation threshold, this network has a broad degree distribution, and at p=p_c the degree…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of…
We study percolation transition of run and tumble particles (RTPs) on a two dimensional square lattice. RTPs in these models run to the nearest neighbour along their internal orientation with unit rate, and to other nearest neighbours with…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
The three-dimensional strongly screened vortex-glass model is studied numerically using methods from combinatorial optimization. We focus on the effect of disorder strength on the ground state and found the existence of a disorder-driven…