  Growing attention has been drawn in the past years to the \alpha-phase (1/3
monolayer) of Sn on Ge(111), which undergoes a transition from the low
temperature (3x3) phase to the room temperature (\sqrt3 x \sqrt3)R30 one. On
the basis of scanning tunnelling microscopy experiments, this transition was
claimed to be the manifestation of a surface charge density wave (SCDW), i.e. a
periodic redistribution of charge, possibly accompanied by a periodic lattice
distortion, which determines a change of the surface symmetry. As further
experiments with different techniques were being performed, increasing doubts
were cast about the SCDW model. We have measured by He scattering the long
range order of the 1/3 monolayer phase of Sn on the Ge(111) surface throughout
the phase transition. The transition has been found of the order-disorder type
with a critical temperature Tc=220 K. The expected 3-State Potts critical
exponents are shown to be consistent with the observed power law dependence of
the (3x3) order parameter and its correlation length close to Tc, thus
excluding a charge density wave driven phase transition.
