  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
cross-over 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.
