  The curvature which characterizes the QCD phase transition at finite
temperature and small values of the chemical potential is accessible to lattice
simulations. The results for this quantity which have been obtained by several
different lattice simulation methods differ due to different numbers of
flavors, different pion masses and different sizes of the simulation volume. In
order to reconcile these results, it is important to investigate finite-volume
effects on the curvature. We investigate the curvature of the chiral phase
transition line at finite temperature and chemical potential in a finite
volume. We use a phenomenological model for chiral symmetry breaking and apply
non-perturbative functional renormalization group methods which account for
critical long-range fluctuations at the phase transition. We find an
intermediate volume region in which the curvature of the phase transition line
is actually reduced relative to its infinite-volume value, provided periodic
spatial boundary conditions are chosen for the quark fields. Size and location
of this region depend on the value of the pion mass. Such an effect could
account for differences in the curvature between lattice simulations in
differently sized volumes and from functional methods in the infinite volume
limit. We discuss implications of our results for the QCD phase diagram.
