  In this work, we study the t-J model using a two-pole approximation within
the composite operator method. We choose a basis of two composite operators --
the constrained electrons and their spin-fluctuation dressing -- and
approximate their currents in order to compute the corresponding Green's
functions. We exploit the algebraic constraints obeyed by the basis operators
to close a set of self-consistent equations that is numerically solved. This
allows to determine the physical parameters of the system such as the spin-spin
correlation function and the kinetic energy. Our results are compared to those
of an exact numerical method on a finite system to asses their reliability.
Indeed, a very good agreement is achieved through a far less numerically
demanding and a more versatile procedure. We show that by increasing the hole
doping, anti-ferromagnetic correlations are replaced by ferromagnetic ones. The
behavior on changing temperature and exchange integral is also studied and
reported.
