PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Spin models on random graphs with controlled topologies beyond degree constraints
Conrad Perez-Vicente and Anthony Coolen
Journal of Physics A Volume 41, 255003, 2008.

Abstract

We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p(k) can be chosen arbitrarily, but which allows for further fine-tuning of the topology via preferential attachment of edges on the basis of an arbitrary function Q(k,k') of the degrees of the vertices involved. We solve these models using finite connectivity equilibrium replica theory, within the replica symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution, but also on the choice made for Q(k,k'). The increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real-world interacting particle systems by spin systems on suitably defined random graphs.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5352
Deposited By:Anthony (Ton) C C Coolen
Deposited On:24 March 2009