CONFORMALLY INVARIANT OBSERVABLES IN THE DOUBLE-DIMER MODEL

The Grassmannian representation of the dimer model is a powerful tool which has already made the computation of the partition function possible in the presence of enough homogeneity. One could also take advantage of this representation to obtain some information about the distribution of double-dimer loops. The double-dimer model is a straightforward generalization of the dimer model, where one considers the geometric picture arising from putting two dimer configurations on each other. In this paper, the authors computed two particular observables defined on double-dimer loops. These are the expectation of the number of loops, and the left-passage probability, when the underlying domain is a rectangular subgraph of the square lattice. They showed that the scaling limits of these observables are related to some specific Green’s functions on the rectangular domains with Dirichlet boundary conditions, which support both the conformal invariance and the relation with the Gaussian free field and conformal loop ensembles with the parameter κ=4.