Ising Model on Connected Complex Networks

Janusz Hołyst , Krzysztof Suchecki

Abstract

Ising dynamics for a system of two weakly connected scale-free networks is analytically investigated using a properly tailored mean field approach. Since order parameters in both networks can be different there are three states of possible spin configurations that correspond to parallel ordered, antiparallel ordered and disordered phases. Transition temperatures between these states are calculated. There is a first-order (discontinuous) phase transition between a phase when both networks possess opposite order parameters and a phase when both networks are parallel ordered. At higher temperature a continuous transition to a paramagnetic phase takes place. The temperature of the first-order phase transition diminishes with the increasing inter-network links density and it becomes zero when the density reaches a critical value. Analytical results based on mean-field approximation are backed up in part with numerical Monte-Carlo simulations.
Author Janusz Hołyst (FP / LPESS)
Janusz Hołyst,,
- Center of Physics in Economics and Social Sciences
, Krzysztof Suchecki (FP / LPESS)
Krzysztof Suchecki,,
- Center of Physics in Economics and Social Sciences
Corporate authorThe Faculty of Physics, WUT (WF), Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB)
Pages167-200
Publication size in sheets1.65
Book Holovatch Yurij (eds.): Order, Disorder and Criticality: Advanced Problems of Phase Transition Theory - Volume 3, 2013, Singapore, World Scientific Publishing Co Pte Ltd, ISBN 9789814417884, 200 p., DOI:10.1142/9789814417891_0004
DOIDOI:10.1142/9789814417891_0004
URL http://www.worldscientific.com/doi/abs/10.1142/9789814417891_0004
Languageen angielski
Score (nominal)5
ScoreMinisterial score = 5.0, 11-05-2020, MonographChapterAuthor
Publication indicators Scopus Citations = 2
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