  We report spin wave and DMRG studies of the ground and low-lying excited
states of uniform and dimerized alternating spin chains. The DMRG procedure is
also employed to obtain low-temperature thermodynamic properties of the system.
The ground state of a 2N spin system with spin-1 and spin-1/2 alternating from
site to site and interacting via an antiferromagnetic exchange is found to be
ferrimagnetic with total spin $s_G=N/2$ from both DMRG and spin wave analysis.
Both the studies also show that there is a gapless excitation to a state with
spin $s_G-1$ and a gapped excitation to a state with spin $s_G+1$.
Surprisingly, the correlation length in the ground state is found to be very
small from both the studies for this gapless system. For this very reason, we
show that the ground state can be described by a variational ``ansatz'' of the
product type. DMRG analysis shows that the chain is susceptible to a
conditional spin-Peierls' instability. The DMRG studies of magnetization,
magnetic susceptibility ($\chi$) and specific heat show strong magnetic-field
dependence. The product $\chi T$ shows a minimum as a function of
temperature($T$) at low-magnetic fields and the minimum vanishes at
high-magnetic fields. This low-field behaviour is in agreement with earlier
experimental observations. The specific heat shows a maximum as a function of
temperature and the height of the maximum increases sharply at high magnetic
fields. It is hoped that these studies will motivate experimental studies at
high-magnetic fields.
