2004/04/30 by Tommaso Rizzo, Rizzo, Tommaso
Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0404729
16 pages, two figures, corrected typos and discussion rewritten
openalex publication_date 2004/04/30 · arxiv created 2004/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theory for the complexity of the Bethe lattice spin-glass is developed applying to the cavity-method scheme of Mezard and Parisi the results recently obtained in the context of the Sherrington-Kirkpatrick model. The crucial ingredient is the introduction of a new cavity field z related to the marginality of the relevant states. The theory admits a variational formulation. In the high-connectivity limit it yields the Bray and Moore expression for the TAP complexity of the SK model. An annealed version of the theory is also studied in order to obtain non-trivial results at low computational cost. An analysis of the theory is performed numerically through population-dynamics algorithms and analytically through power series expansion. The results can be applied to other finite connectivity problems.