Cluster properties of the one-dimensional lattice gas: The microscopic meaning of grand potential
AbstractUsing a concrete example, we demonstrate how the combinatorial approach to a general system of particles, which was introduced in detail in an earlier paper, works and where this approach provides a genuine extension of results obtained through more traditional methods of statistical mechanics. We study the cluster properties of a one-dimensional lattice gas with nearest-neighbor interactions. Three cases (the infinite temperature limit, the range of finite temperatures, and the zero temperature limit) are discussed separately, yielding interesting results and providing alternative proof of known results. In particular, the closed-form expression for the grand partition function in the zero temperature limit is obtained, which results in the nonanalytic behavior of the grand potential, in accordance with the Yang-Lee theory. © 2013 American Physical Society.
|Journal series||Physical Review E, ISSN 1539-3755|
|Publication size in sheets||0.3|
|Keywords in English||Closed-form expression; Cluster property; Combinatorial approach; Finite temperatures; General systems; Grand potential; Nearest-neighbor interactions; One-dimensional lattice; Partition functions; Temperature limits; Yang-Lee theory; Zero temperatures, Crystal lattices; Statistical mechanics, Temperature|
|ASJC Classification||; ;|
|Score|| = 35.0, 01-02-2020, ArticleFromJournal|
= 35.0, 01-02-2020, ArticleFromJournal
|Publication indicators||= 5; = 5; : 2014 = 1.123; : 2013 = 2.326 (2) - 2013=2.302 (5)|
|Citation count*||5 (2015-07-21)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.