General criterion applicable to exclusion processes with an Ising-like invariant measure

• Published in: Chinese journal of physics (Taipei) 2024-04, Vol.88, p.618-631
• Main Authors: Ngoc, Ngo Phuoc Nguyen, Thi, Huynh Anh
• Format: Article
• Language: English
• Subjects: Exclusion process; Ising measure; Ising model; Misanthrope process; Zero-range process
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2024.01.001

This paper explores extensions of the totally asymmetric simple exclusion process in one dimension, assuming periodic boundary conditions. Specifically, we investigate situations where a particle’s movement rate is influenced by the positions of its two nearest neighbors. We establish the necessary and sufficient conditions for these exclusion processes to maintain an Ising-like measure as their invariant measure. Our analysis covers several renowned models, such as the cooperative exclusion process (Antal and Schütz, 2000), its dual model (Gabel and Redner, 2011), the Katz–Lebowitz–Spohn model (Katz et al., 1984), and the facilitated exclusion process (Basu and Mohanty, 2009; Gabel et al., 2010). To compare the obtained models, we will examine the average particle velocity and flux. Upon doing so, we highlight that this research contributes to the comprehension of the collective pushing phenomenon observed, for example, in biological traffic models (Epshtein and Nudler, 2003; Epshtein et al., 2003). [Display omitted] •Ising-like measure naturally emerges in exclusion processes.•General criterion for Ising-like invariant measure in exclusion processes.•Encompassing prominent models like Katz–Lebowitz–Spohn.•Clarifying the collective pushing phenomenon’s nature.