Search for critical points in the SU(2) Higgs model

We study the order of the Higgs phase transition in the SU(2) Higgs model at several values of the gauge coupling $\beta$ for bare quartic coupling $\lambda =0.5\mathrm{}$ using Monte Carlo simulations. We determine the internal energy of metastable states on various lattice sizes and estimate that the transition terminates at the critical point located at $1.95<\mathrm{}{\beta }_c<2.25\mathrm{}$. We also apply a recently proposed multihistogram method in our data analysis. At $\beta =2.25\mathrm{}$ and $\beta =2.4\mathrm{}$ our data strongly indicate the presence of a first-order phase transition. For $\beta \ge 2.6$ we find no indication of a discontinuity in the internal energy on lattices up to size ${16}^4$ and the transition is either weakly first order or of higher order.