Semiflexible fully packed loop model and interacting rhombus tilings.

Motivated by a recent adsorption experiment [M. O. Blunt, Science 322, 1077 (2008)10.1126/science.1163338], we study tilings of the plane with three different types of rhombi. An interaction disfavors pairs of adjacent rhombi of the same type. This is shown to be a special case of a model of fully packed loops with interactions between monomers at distance two along a loop. We solve this model using Coulomb gas techniques and show that its critical exponents vary continuously with the interaction strength. At low temperature it undergoes a Kosterlitz-Thouless transition to an ordered phase, which is predicted from numerics to occur at a temperature T approximately 110 K in the experiments.