Solvable critical dense polymers on the cylinder

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 YangBaxter integrable series of logarithmic minimal models. The cylinder topology allows for non-contractible loops with fugacity - 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 TemperleyLieb algebra, we set up commuting transfer matrices acting on states whose links are considered distinct with respect to connectivity around the front or back of the cylinder. These transfer matrices satisfy a functional equation in the form of an inversion id..