Thermal phase transition with full 2-loop effective potential

Theories with extended Higgs sectors constructed in view of cosmological ramifications (gravitational wave signal, baryogenesis, dark matter) are often faced with conflicting requirements for their couplings; in particular those influencing the strength of a phase transition may be large. Large couplings compromise perturbative studies, as well as the high-temperature expansion that is invoked in dimensionally reduced lattice investigations. With the example of the inert doublet extension of the Standard Model (IDM), we show how a resummed 2-loop effective potential can be computed without a high-T expansion, and use the result to scrutinize its accuracy. With the exception of $T_c$, which is sensitive to contributions from heavy modes, the high-T expansion is found to perform well. 2-loop corrections weaken the transition in IDM, but they are moderate, whereby a strong transition remains an option.