# Logarithmic Minimal Models

*Statistical Mechanics/Combinatorics Seminar*

*by Paul Pearce (Work with Jorgen Rasmussen and Jean-Bernard Zuber)*

*Institution:*Department of Mathematics and Statistics, The University of Melbourne

*Date: Thu 3rd August 2006*

*Time: 3:15 PM*

*Location: Room G05, Dept. of Mathematics and Statistics, Richard Berry Building, The University of Melbourne*

*Abstract*: The planar Temperley-Lieb algebra and link states are used to build Yang-Baxter integrable lattice models called logarithmic minimal models LM(p,p').

The continuum scaling limit of these models is described by 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 the logarithmic Ising model (m=3, c=1/2).

For the principal series on the strip, 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=1,2,...,m; s=1,2,.... The associated conformal partition functions are given in terms of the Virasoro characters of

quasi-rational(highest-weight) representations. We show in particular examples how

fusing quasi-rational representations leads to indecomposable representations.

*For More Information:* Dr. Iwan Jensen Phone: +61 3 8344 5214 I.Jensen@ms.unimelb.edu.au