Logarithmic minimal models

Pearce, Paul A., Rasmussen, Jorgen and Zuber, Jean-Bernard (2006) Logarithmic minimal models. Journal of Statistical Mechanics, 11 Article #P11017: . doi:10.1088/1742-5468/2006/11/P11017

Author Pearce, Paul A.
Rasmussen, Jorgen
Zuber, Jean-Bernard
Title Logarithmic minimal models
Journal name Journal of Statistical Mechanics   Check publisher's open access policy
ISSN 1742-5468
Publication date 2006-11
Sub-type Article (original research)
DOI 10.1088/1742-5468/2006/11/P11017
Issue 11 Article #P11017
Total pages 37
Place of publication Bristol, England, U.K.
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
Working in the dense loop representation, we use the planar Temperley–Lieb algebra to build integrable lattice models called logarithmic minimal models {\cal LM}(p,p') . Specifically, we construct Yang–Baxter integrable Temperley–Lieb models on the strip acting on link states and consider their associated Hamiltonian limits. These models and their associated representations of the Temperley–Lieb algebra are inherently non-local and not (time-reversal) symmetric. We argue that, in the continuum scaling limit, they yield logarithmic conformal field theories with central charges c = 1−(6(p−p')2/pp'), where p, p' = 1, 2, ... are coprime. The first few members of the principal series {\cal LM}(m,m+1) are critical dense polymers (m = 1, c = −2), critical percolation (m = 2, c = 0) and the logarithmic Ising model (m = 3, c = 1/2). For the principal series, we find an infinite family of integrable and conformal boundary conditions organized in an extended Kac table with conformal weights Δr,s = (((m+1)r−ms)2−1)/4m(m+1), r, s = 1, 2, .... The associated conformal partition functions are given in terms of Virasoro characters of highest-weight representations. Individually, these characters decompose into a finite number of characters of irreducible representations. We show with examples how indecomposable representations arise from fusion.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 77 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 14 Mar 2012, 14:40:39 EST by Kay Mackie on behalf of School of Mathematics & Physics