Related papers: Phase transitions in a complex network

We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…

By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…

One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…

The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring,…

In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…

We study networks that display community structure -- groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence…

The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…

We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…

Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of…

We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…

We discuss the hierarchy of subphase transitions in first-order-like nucleation processes for an exemplified aggregation transition of heteropolymers. We perform an analysis of the microcanonical entropy, i.e., the density of states is…

We study the asymptotic behaviour of Markov processes on large weighted Erdos-Renyi graphs where the transition rates of the vertices are only influenced by the state of their neighbours and the corresponding weight on the edges. We find…

We study the change in topological entanglement entropy that occurs when a two-dimensional system in a topologically ordered phase undergoes a transition to another such phase due to the formation of a Bose condensate. We also consider the…

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a…

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

An important source of high clustering coefficient in real-world networks is transitivity. However, existing approaches for modeling transitivity suffer from at least one of the following problems: i) they produce graphs from a specific…