be defined through the equations$$\frac{\partial }{\partial v_{i}}V_{eff}\left( v_{i},T_{c}\right)
=0,~V_{eff}\left( v_{1},v_{2},v_{3},v_{4},T_{c}\right) =V_{eff}\left(
0,0,x_{1},x_{2},T_{c}\right) ,  \label{TC}$$where $x_{1,2}$ are the real and imaginary parts of the $T$-dependent $x$ given in (\[X0\]).

Numerical results
=================

In the following figures, we show the dependence of the quantity $\upsilon
\left( T_{c}\right) /T_{c}$ in (\[cri\]) on the lightest Higgs mass (in Fig. \[Mhn\] left), and on the lightest neutralino mass (in Fig. \[Mhn\] right), for a random choice of about $10^{6}$ cases in both regions **(1)** and **(2)**. We find that only about 8% of the benchmarks fulfill the required conditions, and only 2.5% of the survived benchmarks give a strong first-order phase transition.

![*The dependence of the quantity $\protect\upsilon _{c}/T_{c}$ on the lightest Higgs mass, on the lightest neutralino mass, and the corresponding critical temperature, taking into account different values of the parameters in (\[pra\]) is shown. The red points refer to benchmarks from region **(1)**, and the green ones to benchmarks from region **(2).***[]{data-label="Mhn"}](f1.eps "fig:"){width="8.5cm" height="6.5cm"}  ![*The dependence of the quantity $\protect\upsilon _{c}/T_{c}$ on the lightest Higgs mass, on the lightest neutralino mass, and the corresponding critical temperature, taking into account different values of the parameters in (\[pra\]) is shown. The red points refer to 