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Pré-Publication, Document De Travail Année : 2017

The free-fermionic $C^{(1)}_2$ loop model, double dimers and Kashaev's recurrence

Résumé

We study a two-color loop model known as the $C^{(1)}_2$ loop model. We define a free-fermionic regime for this model, and show that under this assumption it can be transformed into a double dimer model. We then compute its free energy on periodic planar graphs. We also study the star-triangle relation or Yang-Baxter equations of this model, and show that after a proper parametrization they can be summed up into a single relation known as Kashaev's relation. This is enough to identify the solution of Kashaev's relation as the partition function of a $C^{(1)}_2$ loop model with some boundary conditions, thus solving an open question of Kenyon and Pemantle about the combinatorics of Kashaev's relation.
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Dates et versions

hal-01574018 , version 1 (09-11-2018)

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Paul Melotti. The free-fermionic $C^{(1)}_2$ loop model, double dimers and Kashaev's recurrence. 2017. ⟨hal-01574018⟩
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