Matrix product states of three families of one-dimensional interacting particle systems

Farhad H Jafarpour

Physica A: Statistical Mechanics and its Applications, 2004, vol. 339, issue 3, 369-384

Abstract: The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in N. J. Phys. 5 (2003) 145.1, are studied using a matrix product formalism. It is shown that their associated quadratic algebras have two-dimensional representations, provided that the transition rates lie on specific manifolds of parameters. Exact expressions for the correlation functions of each model have also been obtained. We have also studied the steady-state properties of one of these models, first introduced in J. Phys. A: Math. Gen. A 36 (2003) 74, with more details. By introducing a canonical ensemble we calculate the canonical partition function of this model exactly. Using the Yang–Lee theory of phase transitions we spot a second-order phase transition from a power law to a jammed phase. The density profile of particles in each phase has also been studied. A simple generalization of this model in which both the left and the right boundaries are open has also been introduced. It is shown that double shock structures may evolve in the system under certain conditions.

Keywords: Matrix product formalism; Yang–Lee theory (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437104002675
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:339:y:2004:i:3:p:369-384

DOI: 10.1016/j.physa.2004.03.009

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().