205 research outputs found
A statistical mechanics approach for scale-free networks and finite-scale networks
We present a statistical mechanics approach for the description of complex
networks. We first define an energy and an entropy associated to a degree
distribution which have a geometrical interpretation. Next we evaluate the
distribution which extremize the free energy of the network. We find two
important limiting cases: a scale-free degree distribution and a finite-scale
degree distribution. The size of the space of allowed simple networks given
these distribution is evaluated in the large network limit. Results are
compared with simulations of algorithms generating these networks.Comment: (6 pages, 5 figures
Interdisciplinary and physics challenges of Network Theory
Network theory has unveiled the underlying structure of complex systems such
as the Internet or the biological networks in the cell. It has identified
universal properties of complex networks, and the interplay between their
structure and dynamics. After almost twenty years of the field, new challenges
lie ahead. These challenges concern the multilayer structure of most of the
networks, the formulation of a network geometry and topology, and the
development of a quantum theory of networks. Making progress on these aspects
of network theory can open new venues to address interdisciplinary and physics
challenges including progress on brain dynamics, new insights into quantum
technologies, and quantum gravity.Comment: (7 pages, 4 figures
Superconductor-insulator transition in a network of 2d percolation clusters
In this paper we characterize the superconductor-insulator phase transition
on a network of 2d percolation clusters. Sufficiently close to the percolation
threshold, this network has a broad degree distribution, and at p=p_c the
degree distribution becomes scale-free. We study the Transverse Ising Model on
this complex topology in order to characterize the superconductor-insulator
transition in a network formed by 2d percolation clusters of a superconductor
material. We show, by a mean-field treatment, that the critical temperature of
superconductivity depends on the maximal eigenvalue of the adjacency matrix of
the network. At the percolation threshold, we find that the maximal eigenvalue
of the adjacency matrix of the network of 2d percolation clusters has a
maximum. In correspondence of this maximum the superconducting critical
temperature T_c is enhanced. These results suggest the design of new
superconducting granular materials with enhanced critical temperature.Comment: (6 pages, 6 figures
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