تقرير
p-star models, mean field random networks and the heat hierarchy
| العنوان: | p-star models, mean field random networks and the heat hierarchy |
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| المؤلفون: | Biondini, Gino, Moro, Antonio, Prinari, Barbara, Senkevich, Oleg |
| سنة النشر: | 2021 |
| المجموعة: | Condensed Matter Nonlinear Sciences |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Pattern Formation and Solitons, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | We consider the mean field analog of the p-star model for homogeneous random networks, and compare its behaviour with that of the p-star model and its classical mean field approximation in the thermodynamic regime. We show that the partition function of the mean field model satisfies a sequence of partial differential equations known as the heat hierarchy, and the models connectance is obtained as a solution of a hierarchy of nonlinear viscous PDEs. In the thermodynamic limit, the leading order solution develops singularities in the space of parameters that evolve as classical shocks regularised by a viscous term. Shocks are associated with phase transitions and stable states are automatically selected consistently with the Maxwell construction. The case p = 3 is studied in detail. Monte Carlo simulations show an excellent agreement between the p-star model and its mean field analog at the macroscopic level, although significant discrepancies arise when local features are compared. Comment: 12 pages, 9 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevE.105.014306 |
| URL الوصول: | http://arxiv.org/abs/2105.09479 |
| رقم الأكسشن: | edsarx.2105.09479 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevE.105.014306 |
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