Phase diagram of the lattice SU(2) Higgs model

We perform a detailed study of the phase diagram of the lattice Higgs SU(2) model with fixed Higgs field length. Consistently with previsions based on the Fradkin–Shenker theorem we find a first order transition line with an endpoint whose position we determined. The diagram also shows cross-over lines: the crossover corresponding to the pure SU(2) bulk is also present at nonzero coupling with the Higgs field and merges with the one that continues the line of first order transition beyond the critical endpoint. At high temperature the first order line becomes a crossover, whose position moves by varying the temperature.