Logarithmic minimal models

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 Deltaₑ, ₒ= ( ( (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.