Szczegóły publikacji
Opis bibliograficzny
Mean-field approximation for structural balance dynamics in heat bath / Krzysztof MALARZ, Janusz A. Hołyst // Physical Review. E ; ISSN 2470-0045. — Tytuł poprz.: Physical Review E, Statistical, nonlinear, and soft matter physics ; ISSN: 1539-3755. — 2022 — vol. 106 iss. 6 art. no. 064139, s. 064139-1–064139-9. — Bibliogr. s. 064139-8–064139-9, Abstr. — Publikacja dostępna online od: 2022-12-30
Autorzy (2)
- AGHMalarz Krzysztof
- Hołyst Janusz A.
Dane bibliometryczne
| ID BaDAP | 144461 |
|---|---|
| Data dodania do BaDAP | 2023-01-11 |
| Tekst źródłowy | URL |
| DOI | 10.1103/PhysRevE.106.064139 |
| Rok publikacji | 2022 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Physical Review, E |
Abstract
A critical temperature for a complete signed graph of N agents where the time-dependent polarization of links tends towards the Heider (structural) balance is found analytically using the heat-bath approach and the mean-field approximation as Tc=(N−2)/ac, where ac≈1.71649. The result is in perfect agreement with numerical simulations starting from the paradise state where all links are positively polarized as well as with the estimation of this temperature received earlier with much more sophisticated methods. When heating the system, one observes a discontinuous and irreversible phase transition at Tc from a nearly balanced state when the mean link polarization is about xc=0.796388 to a disordered and unbalanced state where the polarization vanishes. When the initial conditions for the polarization of links are random, then at low temperatures a balanced bipolar state of two mutually hostile cliques exists that decays towards the disorder and there is a discontinuous phase transition at a temperature Td that is lower than Tc. The system phase diagram corresponds to the so-called fold catastrophe when a stable solution of the mean-field equation collides with a separatrix, and as a result a hysteresislike loop is observed.
