Abstract We present simple description of a system with two bilinearly coupled order parameters in external field based on an exact mean-field solution of the Landau Hamiltonian. It reproduces the qualitative form of the "field-temperature" phase diagram given by a molecular-field model and by more sophisticated theories and experiments on metamagnets. The solution gives the same critical exponents as the molecular-field theory, but it is not restricted to the magnetic systems only and it is easier to handle, since it formulates the results in explicit analytical form. The susceptibility in this model does not diverge at the second order transition line (far from a higher order critical point separating the second and first order transition lines), but jumps down from the lower temperature wing to the higher temperature one. The jump amplitude is proportional to the square of the field in small fields and diverges in large fields close to the higher order critical point.
Scaling theory for the free-energy barrier to homogeneous nucleation of a noncritical phase near a critical point