  The future space-borne gravitational wave (GW) detectors would provide a
promising probe for the new physics beyond the standard model that admits the
first-order phase transitions. The predictions for the GW background vary
sensitively among different concrete particle physics models but also share a
large degeneracy in the model buildings, which motivates an effective model
description on the phase transition based on different patterns of the
electroweak symmetry breaking (EWSB). In this paper, using the scalar $N$-plet
model as a demonstration, we propose an effective classification for three
different patterns of EWSB: (1) radiative symmetry breaking with classical
scale invariance, (2) Higgs mechanism in generic scalar extension, and (3)
higher dimensional operators. We conclude that a strong first-order phase
transition could be realized for (1) and (2) with a small quartic coupling and
a small isospin of an additional $N$-plet field for the light scalar field
model with and without the classical scale invariance, and (3) with a large
mixing coupling between scalar fields and a large isospin of the $N$-plet field
for the heavy scalar field model.
