  We argue that the t-J model and the recently proposed Ising version of this
model give the same physical picture of the Nagaoka regime for J/t << 1. In
particular, both models are shown to give compatible results for a single
Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the
standard t-J or t-Jz models, the Ising version allows for a numerical analysis
on much larger clusters by means of classical Monte Carlo simulations. Taking
the advantage of this fact, we study the low doping regime of t-J model for J/t
<< 1 and show that the ground state exhibits phase separation into hole-rich
ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds
true up to a threshold concentration of holes, \delta < \delta_t ~ 0.44
\sqrt{J/t}. Analytical calculations show that \delta_t=\sqrt{J/2\pi t}.
