The effect of an external magnetic field on an antiferromagnetic two-dimensional square Ising model with anisotropic nearest neighbour interaction

An analytic expression for the phase boundary equation of the two-dimensional antiferromagnetic Ising square lattice with anisotropic nearest neighbour (Jx ̸= Jy) interactions under the influence of a constant external magnetic field (h) is derived using the domain wall method. The system undergoes an order-disorder phase transition at a critical temperature T = Tc that is given by the condition: e^ ((−2Jy+2h−4ph)/kbTc) (1 − e^(4Jx/kbTc)) = 1 + e^(4Jx/kbTc) + e^((2Jx+2h)/kbTc) + e^((2Jx−2h)/kbTc). The phase diagram for this condition is also derived. For vanishing magnetic field Onsager’s famous result, i.e. sinh(2Jx/kbTc) sinh(2Jy/kbTc) = 1 is recaptured. We also show that the domain wall method is exact and we conjecture that the entire system can be described by a domain wall of minimal length.