θ-vacuum systems via real action simulations

Inspired by the results of the Ising model within an imaginary external magnetic field, we introduce a transformation in quantum systems with a θ-vacuum term that amounts to a rescaling of z=cos θ2. Making use of this transformation we are able to determine the order parameter as a function of θ. The approach is successfully tested in models with both broken and unbroken CP symmetry at θ=π.