  Using the method which retains the rotation symmetry of spin components in
the paramagnetic state and has no preset magnetic ordering, spectral and
magnetic properties of the two-dimensional t-J model in the normal state are
investigated for the ranges of hole concentrations 0 <= x <= 0.16 and
temperatures 0.01t <= T <= 0.2t. The used hopping t and exchange J parameters
of the model correspond to hole-doped cuprates. The obtained solutions are
homogeneous which indicates that stripes and other types of phase separation
are not connected with the strong electron correlations described by the model.
A series of nearly equidistant maxima in the hole spectral function calculated
for low T and x is connected with hole vibrations in the region of the
perturbed short-range antiferromagnetic order. The hole spectrum has a
pseudogap in the vicinity of (0,\pi) and (\pi,0). For x \approx 0.05 the shape
of the hole Fermi surface is transformed from four small ellipses around
(\pm\pi/2,\pm\pi/2) to two large rhombuses centered at (0,0) and (\pi,\pi). The
calculated temperature and concentration dependencies of the spin correlation
length and the magnetic susceptibility are close to those observed in cuprate
perovskites. These results offer explanations for the observed scaling of the
static uniform susceptibility and for the changes in the spin-lattice
relaxation and spin-echo decay rates in terms of the temperature and doping
variations in the spin excitation spectrum of the model.
