  We investigate the Higgs transition within the four dimensional $SU(2)-$
gauge-Higgs model in search for an order parameter as a function of the Higgs
field hopping parameter, $\kappa$, using Lattice technique. We measure the
Higgs condensate after applying Landau Gauge Fixing and study the corresponding
susceptibility, magnetization and fourth order Binder cumulant using four
different spatial volumes with $N_\tau =2$. The computation is carried out with
gauge coupling, $\beta_g = 8$, for a range of scalar self-coupling, $\lambda =
\{0.00010, 0.00350\}$, with emphasis near the critical end-point. Finite size
scaling analysis of the gauge fixed condensate and its cumulants agree with the
standard $3$d Ising values $\nu=0.62997$, $\beta/\nu=0.518$, $\gamma/\nu=1.964$
at $\lambda = 0.00150$. These results are in agreement with previous studies
suggesting $3$d Ising universality class. The numerical results also indicate
that, at the transition point, the gauge fixed condensate vanishes in the
infinite volume limit.

High Energy Physics - Lattice;High Energy Physics - Phenomenology;High Energy Physics - Theory