Modular invariant partition function of critical dense polymers

Understand

A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus.

• More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random cluster models.
• Starting with a cylinder, the commuting periodic single-row transfer matrices are built from the periodic Temperley-Lieb algebra extended by the shift operators Omega and Omega^{-1}.
• In this enlarged algebra, the non-contractible loop fugacity is alpha and the contractible loop fugacity is beta.