Square lattice Ising antiferromagnet in an external magnetic field

We study the anisotropic square lattice Ising antiferromagnet in terms of three parameters: an external magnetic field B, an effective temperature lambda and an anisotropy parameter K. The model, i.e. partition function and free energy, is solved exactly in the anisotropic limit, K → 0, for arbitrary temperature and field by using the transfer matrix method. We also calculate the first corrections beyond this limit. The limit is non trivial and the phase transition is comepletely preserved. It is of the expected Ising type. The transition temperature lambdasub(c)(B,K) is determined excatly for both K → 0 and K → infinitely and the results are used to check the validity of a recently conjectured formula by Mueller-Hartmann and the author. (orig.)