Related papers: Disordered configurations of the Glauber model in …
We investigate the dynamic behavior of lattices with disorder introduced through non-local network connections. Inspired by the Watts-Strogatz small-world model, we employ a single parameter to determine the probability of local connections…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
The zero-temperature Glauber dynamics of the ferromagnetic Ising model on small-world networks, rewired from a two-dimensional square lattice, has been studied by numerical simulations. For increasing disorder in finite networks, the…
We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either A or B, is updated according to the majority rule or zero-temperature Glauber dynamics, in which…
We investigate two competing contact processes on a set of Watts--Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of $N$ sites, where each site $i$ is directly…
We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $\alpha$ controls the probability proportional to…
Blending ordering within an uncorrelated disorder potential in families of 3D Lieb lattices preserves the macroscopic degeneracy of compact localized states and yields unconventional combinations of localized and delocalized phases -- as…
Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper…
We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that…
Disordered spatial networks describe structures and interactions across multiple length scales. The scattering and interference of waves within these networks result in structural phase transitions, localization, diffusion, and band gaps.…
The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of…
The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered…
We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a…
We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber…
We study the evolution of a social network with friendly/enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
We investigate the localization behavior of electrons in a random lattice which is constructed from a quasi-one-dimensional chain with large coordinate number $Z$ and rewired bonds, resembling the small-world network proposed recently but…