Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-09-07
Physics
Condensed Matter
Statistical Mechanics
30 pages, 4 figures
Scientific paper
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved.
Agliari Elena
Barra Adriano
No associations
LandOfFree
Equilibrium statistical mechanics on correlated random graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Equilibrium statistical mechanics on correlated random graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equilibrium statistical mechanics on correlated random graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-704921