The semiflexible fully-packed loop model and interacting rhombus tilings

TL;DR

This paper analyzes a model of plane tilings with three rhombus types, revealing a phase transition and continuous critical exponents influenced by interactions, with implications for adsorption experiments.

Contribution

It introduces a solvable interacting rhombus tiling model linked to fully-packed loops, demonstrating continuous critical exponents and a Kosterlitz-Thouless transition.

Findings

Critical exponents vary continuously with interaction strength.

The model exhibits a Kosterlitz-Thouless transition at low temperature.

Predicted transition temperature aligns with experimental data.

Abstract

Motivated by a recent adsorption experiment [M.O. Blunt et al., Science 322, 1077 (2008)], 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 the latter model using Coulomb gas techniques and show that its critical exponents vary continuously with the interaction strenght. At low temperature it undergoes a Kosterlitz-Thouless transition to an ordered phase, which is predicted from numerics to occur at a temperature T \sim 110K in the experiments.