Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2006

Logarithmic Minimal Models

Résumé

Working in the dense loop representation, we use the planar Temperley-Lieb algebra to build integrable lattice models called logarithmic minimal models 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. 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 LM(m,m+1) are critical dense polymers (m=1, c=-2), critical percolation (m=2, c=0) and 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 Delta_{r,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 which individually decompose into a finite number of irreducible representations. We show with examples how indecomposable representations arise from fusion.

Dates et versions

hal-00101696 , version 1 (27-09-2006)

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Citer

Paul A. Pearce, Jorgen Rasmussen, Jean-Bernard Zuber. Logarithmic Minimal Models. Journal of Statistical Mechanics: Theory and Experiment, 2006, pp.P11017. ⟨hal-00101696⟩
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