the scalar vevs on the temperature $T$ below and just above the critical temperature. We will also check  how could this behavior be changed with respect to the charges $Q^{\prime }$s, and other parameters like $A_{t}$, and $M_{1}^{\prime }$, that appear in the effective potential at one-loop level. Therefore we consider the benchmarks in Table-\[Tab\].

         (a)         (b)         (c)         (d)
  -- ----------- ----------- ----------- -----------
       0.0235      0.0235      0.0235      0.0235
       2.0566      2.0566      2.0566      2.0566
      -208.9569   -208.9569   -208.9569   -208.9569
      1173.3560   1173.3560   1173.3560   1173.3560
       0.3575       1.75       0.3575      0.3575
       1.6147        1.5       1.6147      1.6147
       0.5888      0.5888      0.5888      0.5888
      857.9520    857.9520    857.9520      1500
      398.7435    398.7435    398.7435    398.7435
      881.3455    881.3455    881.3455    881.3455
      274.4727    274.4727      1400      274.4727
      103.6387    326.2436    302.9225    100.8061
       2.5836      0.1940      0.1976      2.6356
      172.1886    163.3732    173.0714    172.1589
       5.6907      5.6569      5.6907      6.2573

  : *The values of the parameters used to study the scalar vevs dependence with respect to the temperature are shown. The mass-dimension parameters are given in GeV.*[]{data-label="Tab"}

From this table, it is clear that the EWPT strength is extremely sensitive to the charges $Q^{\prime }$s which represent in a way the strength of the $%
U(1)^{\prime }$ interactions since the $Q^{\prime }$ charges always appear multiplied by $g^{\prime }$. However, the soft parameter $A_{t}$ and M1 