Related papers: A symmetry breaking transition in the edge/triangl…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (i) the transition of a two-dimensional flow to…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
We consider a sharp interface kinetic model of phase transitions accompanied by elastic strain, together with its phase-field realization. Quantitative results for the steady-state growth of a new phase in a strip geometry are obtained and…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
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…
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
We analyze the 3-parameter family of random networks which are uniform on networks with fixed number of edges, triangles, and nodes (between 33 and 66). We find precursors of phase transitions which are known to be present in the asymptotic…
Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and…
We present a novel theoretical framework established by complex network analysis for understanding the phase transition beyond the Landau symmetry breaking paradigm. In this paper we take a two-dimensional metal-insulator transition driven…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…