  Two analytic examples of globally regular non-Abelian gravitating solitons in
the Einstein-Yang-Mills-Higgs theory in (3+1)-dimensions are presented. In both
cases, the space-time geometries are of the Nariai type and the Yang-Mills
field is completely regular and of meron type (namely, proportional to a pure
gauge). However, while in the first family (type I) $X_{0} = 1/2$ (as in all
the known examples of merons available so far) and the Higgs field is trivial,
in the second family (type II) $X_{0}$ is not 1/2 and the Higgs field is
non-trivial. We compare the entropies of type I and type II families
determining when type II solitons are favored over type I solitons: the VEV of
the Higgs field plays a crucial role in determining the phases of the system.
The Klein-Gordon equation for test scalar fields coupled to the non-Abelian
fields of the gravitating solitons can be written as the sum of a
two-dimensional D'Alembert operator plus a Hamiltonian which has been proposed
in the literature to describe the four-dimensional Quantum Hall Effect (QHE):
the difference between type I and type II solutions manifest itself in a
difference between the degeneracies of the corresponding energy levels.
