  We study in this paper the phase transition in a mobile Potts model by the
use of Monte Carlo simulation. The mobile Potts model is related to a diluted
Potts model which is also studied here by a mean-field approximation. We
consider a lattice where each site is either vacant or occupied by a $q$-state
Potts spin. The Potts spin can move from one site to a nearby vacant site. In
order to study the surface sublimation, we consider a system of Potts spins
contained in a recipient with a concentration $c$ defined as the ratio of the
number of Potts spins $N_s$ to the total number of lattice sites $N_L = N_x
\times N_y \times N_z$. Taking into account the attractive interaction between
the nearest-neighboring Potts spins, we study the phase transition as functions
of various physical parameters such as the temperature, the shape of the
recipient and the spin concentration. We show that as the temperature
increases, surface spins are detached from the solid phase to form a gas in the
empty space. Surface order parameters indicate different behaviors depending on
the distance to the surface. At high temperatures, if the concentration is high
enough, the interior spins undergo a first-order phase transition to an
orientationally disordered phase. The mean-field results are shown as functions
of temperature, pressure and chemical potential, which confirm in particular
the first-order character of the transition.
