Solvable critical dense polymers

Pearce, Paul A. and Rasmussen, Jorgen (2007) Solvable critical dense polymers. Journal of Statistical Mechanics: Theory and Experiment, 2007 P02015.1-P02015.32. doi:10.1088/1742-5468/2007/02/P02015


Author Pearce, Paul A.
Rasmussen, Jorgen
Title Solvable critical dense polymers
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2007-02
Sub-type Article (original research)
DOI 10.1088/1742-5468/2007/02/P02015
Volume 2007
Start page P02015.1
End page P02015.32
Total pages 32
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in the form of an inversion identity satisfied by the commuting double-row transfer matrices. This is established directly in the planar Temperley–Lieb algebra and holds independently of the space of link states on which the transfer matrices act. Different sectors are obtained by acting on link states with s−1 defects where s = 1,2,3,... is an extended Kac label. The bulk and boundary free energies and finite-size corrections are obtained from the Euler–Maclaurin formula. The eigenvalues of the transfer matrix are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields a selection rule for the physically relevant solutions to the inversion identity and explicit finitized characters for the associated quasi-rational representations. In particular, in the scaling limit, we confirm the central charge c = −2 and conformal weights Δs = ((2−s)2−1)/8 for s = 1,2,3,.... We also discuss a diagrammatic implementation of fusion and show with examples how indecomposable representations arise. We examine the structure of these representations and present a conjecture for the general fusion rules within our framework.
Keyword Conformal field theory
Loop models and polymers
Quantum integrability (Bethe ansatz)
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # P02015. Part of Topical articles on The 75th Anniversary of the Bethe Ansatz.

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 14 Mar 2012, 14:20:58 EST by Kay Mackie on behalf of Mathematics