2008/02/29 by Jack Raymond, J R Raymond, David Saad +1
Physics and Astronomy · #Opinion Dynamics and Social Influence #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/32/324014
35 pages, 9 figures, submitted to JPhys A
arxiv created 2008/03/18 · openalex publication_date 2008/07/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical disordered or uniform bond distributions; mixing the models by variation of a parameter γ alongside inverse temperature β we analyse the respective thermodynamic solutions. We describe the variation in high temperature transitions as mixing occurs; in the vicinity of these transitions we exactly analyse the competing effects of the dense and sparse models. By using the replica symmetric ansatz and population dynamics we described the low temperature behaviour of mixed systems.