Phase transitions and relaxation dynamics of Ising models exchanging particles

Segun Goh, Jean-Yves Fortin and M.Y. Choi

Physica A: Statistical Mechanics and its Applications, 2017, vol. 466, issue C, 166-179

Abstract: A variety of systems in nature and in society are open and subject to exchanging their constituents with other systems (e.g., environments). For instance, in biological systems, cells collect necessary energy and material by exchange of molecules or ions. Similarly, countries, cities or research institutes evolve as their constituents move in or out. To probe the corresponding particle exchange dynamics in such systems, we consider two Ising models exchanging particles and establish a master equation describing the equilibrium phases as well as the non-equilibrium dynamics of the system. It is found that an additional stable phase emerges as a consequence of the particle exchange process. Furthermore, we formulate the Ginzburg–Landau theory which allows to probe correlation effects. Accordingly, critical slowing down is manifested and the associated dynamic exponent is computed in the linear relaxation regime. In particular, this approach is relevant for investigating the grand canonical description of the system plus environment, with particle exchange and state transitions taken into account explicitly.

Keywords: Particle exchange; Coupled Ising models; Master equation; Ginzburg–Landau theory (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:466:y:2017:i:c:p:166-179

DOI: 10.1016/j.physa.2016.09.007

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