  We assess experimentally and theoretically the character of the
superfluid-supersolid quantum phase transition recently discovered in trapped
dipolar quantum gases. We find that one-row supersolids can have already two
types of phase transitions, discontinuous and continuous, that are reminiscent
of the first- and second-order transitions predicted in the thermodynamic limit
in 2D and 1D, respectively. The smooth crossover between the two regimes is
peculiar to supersolids and can be controlled via the transverse confinement
and the atom number. We justify our observations on the general ground of the
Landau theory of phase transitions. The quasi-adiabatic crossing of a
continuous phase transition opens new directions of investigation for
supersolids.
