A restricted dimer model on a 2-dimensional random causal triangulation

We introduce a restricted hard dimer model on a random causal triangulation that is exactly solvable and generalizes a model recently proposed by Atkin and Zohren. We show that the latter model exhibits unusual behaviour at its multicritical point; in particular, its Hausdorff dimension equals 3 and not 3/2 as would be expected from general scaling arguments. When viewed as a special case of the generalized model introduced here we show that this behaviour is not generic and therefore is not likely to represent the true behaviour of the full dimer model on a random causal triangulation.