  The t-J model on the square lattice, close to the t-J_z limit, is studied by
quantum Monte Carlo techniques at finite temperature and in the underdoped
regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify
the antiferromagnetic domains on each Trotter slice. The results show that the
model presents at high enough temperature finite antiferromagnetic (AF) domains
which collapse at lower temperatures into a single ordered AF state. While
there are domains, holes would tend to preferentially move along the domain
walls. In this case, there are indications of hole pairing starting at a
relatively high temperature. At lower temperatures, when the whole system
becomes essentially fully AF ordered, at least in finite clusters, holes would
likely tend to move within phase separated regions. The crossover between both
states moves down in temperature as doping increases and/or as the off-diagonal
exchange increases. The possibility of hole motion along AF domain walls at
zero temperature in the fully isotropic t-J is discussed.
