Scaling limit of domino tilings on a pentagonal domain

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model.