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Zbl 1206.82018
Cont, David Dei; Nienhuis, Bernard
The packing of two species of polygons on the square lattice. (English)
[J] J. Phys. A, Math. Gen. 37, No. 9, 3085-3100 (2004). ISSN 0305-4470

Summary: We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24-vertex model which is known in the literature as the fully packed double loop model (FPL2). In the particular case in which the fugacities of the polygons are the same, the model admits an exact solution. The solution is obtained using coordinate Bethe ansatz and provides a closed expression for the free energy. In particular, we find the free energy of the four-colouring model and the double Hamiltonian walk and recover the known entropy of the Ice model. When both fugacities are set equal to 2 the model undergoes an infinite-order phase transition.

MSC 2000:: *82B20 Lattice systems
82B26 Phase transitions (general)
82B41 Random walks, etc. (statistical mechanics)

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Zentralblatt MATH Berlin [Germany]