  Numerical investigations of the XY model, the Heisenberg model and the J-J'
Heisenberg model are conducted, using the exact diagonalisation, the numerical
renormalisation and the density matrix renormalisation group approach. The
low-lying energy levels are obtained and finite size scaling is performed to
estimate the bulk limit values. The results are found to be consistent with the
exact values. The DMRG results are found to be most promising.
  The Schwinger model is also studied using the exact diagonalisation and the
strong coupling expansion. The massless, the massive model and the model with a
background electric field are explored. Ground state energy, scalar and vector
particle masses and order parameters are examined. The achieved values are
observed to be consistent with previous results and theoretical predictions.
Path to the future studies is outlined.
