Spontaneous CP violation on the lattice

At finite temperatures around the electroweak phase transition, the thermodynamics of the MSSM can be described by a three-dimensional two Higgs doublet effective theory. This effective theory has a phase where CP is spontaneously violated. We study spontaneous CP violation with non-perturbative lattice simulations, and analyse whether one could end up in this phase for any physical MSSM parameter values.