  The local properties of the spin one ferromagnetic Blume-Capel model defined
on hierarchical lattices with dimension two and three are obtained by a
numerical recursion procedure and studied as functions of the temperature and
the reduced crystal-field parameter. The magnetization and the density of sites
in the configuration S=0 state are carefully investigated at low temperature in
the region of the phase diagram that presents the phenomenon of phase
reentrance. Both order parameters undergo transitions from the ferromagnetic to
the ordered paramagnetic phase with abrupt discontinuities that decrease along
the phase boundary at low temperatures. The distribution of magnetization in a
typical profile was determined on the transition line presenting a broad
multifractal spectrum that narrows towards the fractal limit (single point) as
the discontinuities of the order parameters grow towards a maximum. The
amplitude of the order-parameter discontinuities and the narrowing of the
multifractal spectra were used to delimit the low temperature interval for the
possible locus of the tricritical point.
