The University of Queensland

Centre for Mathematical Physics

SEMINAR

Speaker: Jorgen Rasmussen, University of Melbourne

Title: Solvable critical dense polymers on the cylinder

12pm, Wednesday 27^th October, 2009

Room 42-115

Abstract:

A lattice model of critical dense polymers is solved exactly on a cylinder with finite circumference. The model is the first member LM(1,2) of the Yang-Baxter integrable series of logarithmic minimal models. The cylinder topology allows for non-contractible loops with fugacity alpha that wind around the cylinder or for an arbitrary number l of defects that propagate along the full length of the cylinder. Using an enlarged periodic Temperley-Lieb algebra, we set up commuting transfer matrices acting on link states. These transfer matrices satisfy a functional equation in the form of an inversion identity which is solved exactly for alpha=2. The eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. In the scaling limit, we obtain the conformal partition functions as sesquilinear forms and confirm the central charge c=-2 and conformal weights Delta=((l/2)^2-1)/8.

All interested are invited to attend.

Enquiries to Phillip Isaac email: psi@maths.uq.edu.au