Coupling of hard dimers to dynamical lattices via random tensors

Abstract

We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the critical behavior of the continuum limit is that of pure random lattices. We find a negative critical activity where the universality class is changed as dimers become critical, in a very similar way to that in which hard dimers exhibit a Yang–Lee singularity on planar dynamical graphs. Critical exponents are calculated exactly. An alternative description as a system of ‘color-sensitive hard-core dimers’ on random branched polymers is provided.