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

TL;DR

This paper introduces an exactly solvable restricted dimer model on 2D random causal triangulations, revealing that unusual multicritical behavior is not generic and likely not representative of the full model.

Contribution

It presents a new exactly solvable restricted dimer model on random causal triangulations and clarifies the non-generic nature of certain multicritical behaviors.

Findings

The model is exactly solvable.

Unusual multicritical behavior is not generic.

Full dimer model likely does not exhibit this behavior.

Abstract

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.