A closure for the master equation starting from the dynamic cavity method. (28th April 2023)

• Record Type: Journal Article
• Authors: Aurell, Erik; Machado Perez, David; Mulet, Roberto
• Is Part Of: Journal of physics. Volume 56:Number 17(2023)
• Publication Date: 2023-04-28
• Subjects: closure -- dynamic cavity -- cavity master equation -- Ising ferromagnet -- Viana–Bray spin glass; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/acc8a4
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner using the theory of Random Point Processes. Within this approach, the master equation governing the system's dynamics is closed via a set of differential equations for the auxiliary cavity probabilities. The numerical results improve on the earlier versions of the closure on several important classes of problems. We re-visit here the cases of the Ising ferromagnet and the Viana–Bray spin-glass model.