| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Rio Grande do Sul, Phys Inst, BR-91501970 Porto Alegre, RS - Brazil
[2] London Math Lab, 8 Margravine Gardens, London W6 8RH - England
[3] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | JOURNAL OF PHYSICS-COMPLEXITY; v. 3, n. 1 MAR 1 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a fundamental tool to tackle this problem and a cornerstone of statistical physics, with an impressive number of applications in condensed matter, biology, and computer science. In this work we derive the mean-field equations for the equilibrium behavior of vector spin models on high-connectivity random networks with an arbitrary degree distribution and with randomly weighted links. We demonstrate that the high-connectivity limit of spin models on networks is not universal in that it depends on the full degree distribution. Such nonuniversal behavior is akin to a remarkable mechanism that leads to the breakdown of the central limit theorem when applied to the distribution of effective local fields. Traditional mean-field theories on fully-connected models, such as the Curie-Weiss, the Kuramoto, and the Sherrington-Kirkpatrick model, are only valid if the network degree distribution is highly concentrated around its mean degree. We obtain a series of results that highlight the importance of degree fluctuations to the phase diagram of mean-field spin models by focusing on the Kuramoto model of synchronization and on the Sherrington-Kirkpatrick model of spin-glasses. Numerical simulations corroborate our theoretical findings and provide compelling evidence that the present mean-field theory describes an intermediate regime of connectivity, in which the average degree c scales as a power c mu N (b) (b < 1) of the total number N >> 1 of spins. Our findings put forward a novel class of spin models that incorporate the effects of degree fluctuations and, at the same time, are amenable to exact analytic solutions. (AU) | |
| FAPESP's process: | 16/23827-6 - Analysis of epidemic and synchronization processes in complex networks |
| Grantee: | Thomas Kaue Dal Maso Peron |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |