  The partition functions for two-dimensional nearest neighbour Ising model in
a non-zero magnetic field have been derived for finite square lattices with the
help of graph theoretical procedures, show-bit algorithm, enumeration of
configurations and transfer matrix methods. A new recurrence relation valid for
all lattice sizes is proposed. A novel method of computing the critical
temperature has been demonstrated. The magnetization and susceptibility for
infinite lattices in the presence of magnetic field is estimated. The critical
exponent {\delta} pertaining to the magnetization has also been computed.
