The partition function for two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived . A comparison with the partition functions predicted by Onsager is carried out. The critical temperature estimated by two different methods yields good agreement with the result of Yang and Lee.
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 δ pertaining to the magnetization has also been computed.