  The spin correlations of the bilayer manganite $La_{1.2}Sr_{1.8}Mn_{2}O_{7}$
have been studied using neutron scattering. On cooling within the paramagnetic
state, we observe purely two-dimensional behavior with a crossover to
three-dimensional scaling close to the ferromagnetic transition. Below $T_C$,
an effective finite size behavior is observed. The quantitative agreement of
these observations with the conventional quasi two-dimensional
Kosterlitz-Thouless model indicates that the phase transition is driven by the
growth of magnetic correlations, which are only weakly coupled to polarons
above $T_C$.
