  The two-dimensional freezing transition is very different from its
three-dimensional counterpart. In contrast, the glass transition is usually
assumed to have similar characteristics in two and three dimensions. Using
computer simulations we show that glassy dynamics in supercooled two- and
three-dimensional fluids are fundamentally different. Specifically, transient
localization of particles upon approaching the glass transition is absent in
two dimensions, whereas it is very pronounced in three dimensions. Moreover,
the temperature dependence of the relaxation time of orientational correlations
is decoupled from that of the translational relaxation time in two dimensions
but not in three dimensions. Lastly, the relationships between the
characteristic size of dynamically heterogeneous regions and the relaxation
time are very different in two and three dimensions. These results strongly
suggest that the glass transition in two dimensions is different than in three
dimensions.
