  We investigate the critical behavior of the S=1/2 alternating Heisenberg
chain using the density matrix renormalization group (DMRG). The ground-state
energy per spin and singlet-triplet energy gap are determined for a range of
alternations. Our results for the approach of the ground-state energy to the
uniform chain limit are well described by a power law with exponent p=1.45. The
singlet-triplet gap is also well described by a power law, with a critical
exponent of p=0.73, half of the ground-state energy exponent. The
renormalization group predictions of power laws with logarithmic corrections
can also accurately describe our data provided that a surprisingly large scale
parameter is present in the logarithm.
