squarks, neutralinos and charginos, respectively.

The thermal corrections to the effective potential can be computed using the known techniques [@Th]. The one-loop effective potential at finite temperature is given by$$V_{eff}\left( h_{1},h_{2},S,T\right) =V^{1-l}\left( h_{1},h_{2},S\right)
+T^{4}\sum_{i}n_{i}J_{B,F}\left( m_{i}^{2}\left( h_{1},h_{2},S\right)
/T^{2}\right) ;  \label{Vt}$$ with$$J_{B,F}\left( \alpha\right) =\frac{1}{2\pi^{2}}\int_{0}^{\infty}x^{2}\log(1%
\mp\exp(-\sqrt{x^{2}+\alpha})),  \label{JBF}$$ $n_{i}$ are given above and $m_{i}^{2}\left( h_{1},h_{2},S\right) $ are given in Appendix A. In this work, to take into account all the heavy and light fields, we will evaluate this integral numerically.

The parameters
--------------

In this model, we have many parameters, some of which are free like: $%
g^{\prime }$, $\lambda $, $\upsilon _{x}$, $\tan \beta =\upsilon
_{1}/\upsilon _{2}$, and the soft terms: $m_{Q}$, $m_{U}$, $A_{t}$, $%
A_{\lambda }$, $M_{2}$, $M_{1}$, and $M_{1}^{\prime }$; and others that are fixed by a measured physical quantities such as : $g_{1}$, $g_{2}$, $%
\upsilon $ and $y_{t}$; or can be conditions like the elimination of $%
m_{1}^{2}$, $m_{2}^{2}$, and $m_{S}^{2}$ in (\[Vv\]).

In scanning the parameter space of this model, we take into account the constraint $Q_{1}+Q_{2}+Q_{s}=0$, conditions from the minimization of the potential, the perturbativity of the quartic couplings in (\[Vv\]), and the vacuum stability (\[Vsta\]). Another constraint could be derived from the upper bound on the 