The study of the universe's primordial plasma at high temperature plays an important role when tackling different questions in cosmology, such as the origin of the matter‐antimatter asymmetry. In the Minimal Standard Model (MSM) neither the amount of CP violation nor the strength of the phase transition are enough to produce and preserve baryon number during the Electroweak Phase Transition (EWPT), which are two of the three ingredients needed to develop baryon asymmetry. In this talk we present the first part of the analysis done within a scenario where it is viable to have improvements to the aforementioned situation: we work with the degrees of freedom in the broken symmetry phase of the MSM and analyze the development of the EWPT in the presence of a weak magnetic field. More specifically, we calculate the particle self‐energies that include the effects of the weak magnetic field, needed for the MSM effective potential up to ring diagrams.