  The phenomenon of spontaneous symmetry breaking admits a physical
interpretation in terms of the Bose-condensation process of elementary spinless
quanta. In a cutoff theory, this leads to a picture of the vacuum as a
condensed medium whose excitations might deviate from exact Lorentz covariance
in both the ultraviolet and infrared regions. For this reason, the conventional
singlet Higgs boson, the shifted field of spontaneous symmetry breaking, rather
than being a purely massive field, might possess a gapless branch describing
the long-wavelength fluctuations of the scalar condensate. To test this idea,
that might have substantial phenomenological implications, I compare with a
detailed lattice simulation of the broken phase in the 4D Ising limit of the
theory. The results are the following: i) differently from the symmetric phase,
the single-particle energy spectrum is not reproduced by the standard massive
form ii) for the value of the hopping parameter \kappa=0.076, increasing the
lattice size from 20^4 to 32^4, the mass gap is found to decrease from the
value 0.392(1) reported by Balog et al. (see Nucl. Phys. B714 (2005) 256) to
the value 0.366(5). Both results confirm that, in the infrared region, the
standard singlet Higgs cannot be considered as a simple massive field. Several
arguments indicate that, approaching the continuum limit of the lattice theory,
the observed volume dependence of the mass gap might require larger and larger
lattice sizes before to show up.
