Interacting Fermions Picture For Dimer Models

Recent numerical results on classical dimers with weak aligning interactions have been theoretically justified via a Coulomb gas representation of the height random variable. Here, we propose a completely different representation, the interacting fermions picture, which avoids some difficulties of the Coulomb gas approach and provides a better account of the numerical findings. Besides, we observe that the Peierls argument explains the behavior of the system in the strong interaction case.