Fully packed loop models on finite geometries

Understand

Fully packed loop models describe the statistics of closely packed nested polygons on the square lattice.

• Many exact results can be obtained for these models, even for finite geometries, using their close relationship to alternating-sign matrices and the solvable six-vertex and O(n=1) lattice models.
• Some results for the exact partition function of fully packed loop models on various finite geometries are briefly reviewed, as well as the well-known order-disorder bulk phase transition present in these models.
• A detailed study is presented of the distribution of boundary nests of polygons in fully packed loop models with mirror or rotational symmetry.