  We provide a framework to study the interfaces imposed by Dobrushin boundary
conditions on the half-plane version of the Ising model on random
triangulations with spins on vertices. Using the combinatorial solution by
Albenque, M\'enard and Schaeffer ([2]) and the generating function methods
introduced by Chen and Turunen ([8], [9]), we show the local weak convergence
of such triangulations of the disk as the perimeter tends to infinity, and
study the interface imposed by the Dobrushin boundary condition. As a
consequence of this analysis, we verify the heuristics of physics literature
that discrete interface of the model in the high-temperature regime resembles
the critical site percolation interface, as well as provide an explicit scaling
limit of the interface length at the critical temperature, which coincides with
results on the continuum Liouville Quantum gravity surfaces. Overall, this
model exhibits simpler structure than the model with spins on faces, as well as
demonstrates the robustness of the methods developed in [8], [9].
