Related papers: Exact results for the Ising model on a small-world…
Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze…
Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. The on-off intermittency is investigated in small-world…
Recent work on random field Ising model is described briefly emphasizing exact solutions of the model in simple cases and their relevance in understanding equilibrium and non-equilibrium properties of systems with quenched disorder.
Familiar laws of physics are applied to study human relations, modelled by their world lines (worldlines, WLs) combined with social networks. We focus upon the simplest, basic element of any society: a married couple, stable due to the…
Markopoulou and Smolin have argued that the low energy limit of LQG may suffer from a conflict between locality, as defined by the connectivity of spin networks, and an averaged notion of locality that emerges at low energy from a…
We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
We write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional…
Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages.…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular…
It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be…
A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the…
We propose a geometric growth model which interpolates between one-dimensional linear graphs and small-world networks. The model undergoes a transition from large to small worlds. We study the topological characteristics by both theoretical…
In this paper, we propose a model enabling the creation of a social graph corresponding to real society. The procedure uses data describing the real social relations in the community, like marital status or number of kids. Results show the…
Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and…