Related papers: Explosive Percolation is Continuous, but with Unus…
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 consider the problem of distinguishing classical (Erd\H{o}s-R\'{e}nyi) percolation from explosive (Achlioptas) percolation, under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…
We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is…
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The…
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…
We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
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…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
A nano-second scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as…
The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…
The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With high-precision simulations of the order parameter and the…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…