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Logarithmic minimal models

P. Pearce,J. Rasmussen,J. Zuber

Published 2006 in Journal of Statistical Mechanics: Theory and Experiment

ABSTRACT

Working in the dense loop representation, we use the planar Temperley–Lieb algebra to build integrable lattice models called logarithmic minimal models . 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 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.

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