Effective approach to the Nagaoka regime of the two-dimensional t-J model

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-J(z) models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking advantage of this fact, we study the low doping regime of the 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) similar or equal to 0.44v root J/t. Analytical calculations show that delta(t) = root J/2 pi t.