  Observations of globular clusters show that they have universal lognormal
mass functions with a characteristic peak at $\sim 2\times 10^{5}\,
{\rm{M_{\odot}}}$, but the origin of this peaked distribution is highly
debated. Here we investigate the formation and evolution of star clusters in
interacting galaxies using high-resolution hydrodynamical simulations performed
with two different codes in order to mitigate numerical artifacts. We find that
massive star clusters in the range of $\sim 10^{5.5} - 10^{7.5}\,
{\rm{M_{\odot}}}$ form preferentially in the highly-shocked regions produced by
galaxy interactions. The nascent cluster-forming clouds have high gas pressures
in the range of $P/k \sim 10^8 - 10^{12}\, \rm{K}\,\rm{cm^{-3}}$, which is
$\sim 10^4 - 10^8$ times higher than the typical pressure of the interstellar
medium but consistent with recent observations of a pre-super star cluster
cloud in the Antennae Galaxies. Furthermore, these massive star clusters have
quasi-lognormal initial mass functions with a peak around $\sim 10^{6}\,
{\rm{M_{\odot}}}$. The number of clusters declines with time due to destructive
processes, but the shape and the peak of the mass functions do not change
significantly during the course of galaxy collisions. Our results suggest that
gas-rich galaxy mergers may provide a favorable environment for the formation
of massive star clusters such as globular clusters, and that the lognormal mass
functions and the unique peak may originate from the extreme high-pressure
conditions of the birth clouds and may survive the dynamical evolution.
