  Gravitational properties of a hedge-hog type topological defect in two extra
dimensions are considered in General Relativity employing a vector as the order
parameter. The developed macroscopic theory of phase transitions with
spontaneous symmetry breaking is applied to the analysis of possible "thick"
brane structures. The previous considerations were done using the order
parameter in the form of a multiplet in a target space of scalar fields. The
difference of these two approaches is analyzed and demonstrated in detail.
  There are two different symmetries of regular solutions of Einstein equations
for a hedgehog type vector order parameter. Both solutions are analyzed in
parallel analytically and numerically. Regular configurations in cases of
vector order parameter have one more free parameter in comparison with the
scalar multiplet solutions. It is shown that the existence of a negative
cosmological constant is sufficient for the spontaneous symmetry breaking of
the initially plain bulk. Regular configurations have a growing gravitational
potential and are able to trap the matter to the brane. Among others there are
solutions with the gravitational potential having several points of minimum.
Identical in the uniform bulk spin-less particles, being trapped within
separate points of minimum, acquire different masses and appear to an observer
within the brane as different particles with integer spins.
