  We report the first application of critical cluster techniques to the Mott
metal-insulator transition in vanadium dioxide. We show that the geometric
properties of the metallic and insulating puddles observed by scanning
near-field infrared microscopy are consistent with the system passing near
criticality of the random field Ising model as temperature is varied. The
resulting large barriers to equilibrium may be the source of the unusually
robust hysteresis phenomena associated with the metal-insulator transition in
this system.
