Related papers: Phase Transitions in the Edge/Concurrent Vertex Mo…
In this work, we investigate the temporal evolution of the degree of a given vertex in a network by mapping the dynamics into a random walk problem in degree space. We analyze when the degree approximates a pre-established value through a…
We consider the discrete-time threshold-$\theta \ge 2$ contact process on a random r-regular graph on n vertices. In this process, a vertex with at least \theta occupied neighbors at time t will be occupied at time t+1 with probability p,…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it…
Compartmental models are the most widely used framework for modeling infectious diseases. These models have been continuously refined to incorporate all the realistic mechanisms that can shape the course of an epidemic outbreak. Building on…
Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested…
A spherical model of skeleton with junctions is investigated by Monte Carlo simulations. The model is governed by one-dimensional bending energy. The results indicate that the model undergoes a first-order transition separating the smooth…
We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2 >0 (second…
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…
We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to multipartite structure, separated by a phase transition from a region of disordered graphs.
We study a random graph model which is a superposition of the bond percolation model on $Z^d$ with probability $p$ of an edge, and a classical random graph $G(n, c/n)$. We show that this model, being a {\it homogeneous} random graph, has a…
We introduce a novel model, comprising self-avoiding surfaces and incorporating edges and tubules, that is designed to characterize the structural morphologies and transitions observed within the endoplasmic reticulum (ER). By employing…
We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis…
In the canonical formalism of statistical physics, a signature of a first order phase transition for finite systems is the bimodal distribution of an order parameter. Previous thermodynamical studies of nuclear sources produced in heavy-ion…
In the context of a random walk on an undirected graph, Kemeny's constant can measure the average travel time for a random walk between two randomly chosen vertices. We are interested in graphs that behave counter-intuitively in regard to…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…
Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…
It is believed at present that the chiral transition changes from a smooth crossover to a first-order transition at low temperatures and high densities. Such regime is commonly analyzed using effective models since first principle…
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or…