2008/03/04 by C. J. Perez-Vicente, C. J. Pérez Vicente, A C C Coolen +1 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/1751-8113/41/25/255003
21 pages, 4 figures, submitted to J Phys A
arxiv created 2008/03/04 · openalex publication_date 2008/05/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.