The t-J model has been proposed to describe the physics of copper oxid
e planes in high-temperature superconductors. A real-space quantum ren
ormalization-group method is developed in order to study the t-J Hamil
tonian in a square lattice. The zero-temperature phase diagram is anal
ysed for electron concentrations near the half-filled band and ratio J
/t. A critical line is found that separates two distinct regions: one
of a gas of holes in an antiferromagnetic background, and the other co
nsisting of a phase in which holes segregate into a hole-rich and a pu
re antiferromagnetic region, as demonstrated by chemical-potential eig
envalue calculations near the phase attractor. The results are close t
o the experimental observations.