Real effective potentials for phase transitions in models with extended scalar sectors

The effective potential obtained by loop expansion is usually not real in the range of field values explored its minima during a phase transition. We apply optimized perturbation theory fixed gauge to singlet scalar extensions Standard Model order calculate one-loop that construction. test this computational scheme comparing such Landau derived based on Higgs pole mass. carry out latter construction imposing physical renormalization conditions, which yields without residual regularization scale dependence. use our study parameter dependence critical temperatures two-step transition form $(0,0)\to (0,w')\to (v,w)$ occurs for decreasing temperature SM with two vacuum expectation $v$ and $w$.