that appear in the effective potential at one loop could have an important effect on the strength of the EWPT for some particular choices of the parameter space. The dependence of the EWPT strength on the relative phase $\theta _{0}
$, could be seen by taking changing its value of the benchmark (a) in Table-\[Tab\]. We find that its effect is extremely negligible \[difference in the value of $\upsilon \left( T_{c}\right) /T_{c}$ is $<$ 0.1%\].

![*The dependence of the scalar vevs on the temperature T is shown. These quantities are scaled by their zero temperature values. The solid curves refer to the broken phase, where (*$\protect\upsilon _{1},%
\protect\upsilon _{2},\protect\upsilon _{x}$*) represents the global minimum. While the dashed ones refer to the symmetric phase, where the global minimum is (0,0,x(T)).*[]{data-label="cs"}](cs.eps){width="16cm" height="13cm"}

In Fig. \[cs\], we show the dependence of the ground state on the temperature below the critical temperature for the benchmark (a) in Table-\[Tab\], and its modifications (b), (c) and (d). One remarks that the common feature between all these cases is that the dependence of the singlet vev on the temperature is very weak around and below the critical temperature. This could be understood due to the fact that 