  We consider infinite random planar maps decorated by the critical
Fortuin-Kasteleyn model with parameter $q>4$. The paper demonstrates that when
appropriately rescaled, these maps converge in law to the infinite continuum
random tree as pointed metric-measure spaces, that is, with respect to the
local Gromov-Hausdorff-Prokhorov topology. Furthermore, we also show that these
maps do not admit any Fortuin-Kasteleyn loops with a macroscopic graph distance
diameter. Our proof is based on Scott Sheffield's hamburger-cheeseburger
bijection.
