Continued fractions and the partially asymmetric exclusion process

R.A. Blythe, W. Janke, D.A. Johnston, Ralph Kenna

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We note that a tridiagonal matrix representation of the algebra of the partially asymmetric exclusion process (PASEP) lends itself to interpretation as the transfer matrix for weighted Motzkin lattice paths. A continued-fraction ('J fraction') representation of the lattice-path-generating function is particularly well suited to discussing the PASEP, for which the paths have height-dependent weights. We show that this not only allows a succinct derivation of the normalization and correlation lengths of the PASEP, but also reveals how finite-dimensional representations of the PASEP algebra, valid only along special lines in the phase diagram, relate to the general solution that requires an infinite-dimensional representation.
Original languageEnglish
Article number325002
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number32
DOIs
Publication statusPublished - 2009

Bibliographical note

The full text is available free from the link given. The published version can be found at http://dx.doi.org/10.1088/1751-8113/42/32/325002.

Keywords

  • phase transitions: general studies
  • matrix theory
  • nonequilibrium and irreversible thermodynamics
  • combinatorics
  • graph theory
  • lattice theory and statistics (Ising
  • Potts
  • etc.)

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