arXiv2023
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, $κ$, 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 $N_τ=2$. The computation is carried out with gauge coupling, $β_g = 8$, for a range of scalar self-coupling, $λ= \{0.00010, 0.00350\}$, 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 $ν=0.62997$, $β/ν=0.518$, $γ/ν=1.964$ at $λ= 0.00150$. 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.