We use an optimized perturbation expansion called the linear delta-expansio
n to study the phase transition in a Higgs sector with a continuous symmetr
y and large couplings. Our results show how to use this non-perturbative me
thod successfully for such problems. We also show how to simplify the metho
d without losing any flexibility. (C) 2000 Elsevier Science B.V. All rights
reserved.