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We compare the role of the three-site terms added to the t-J models in theSU(2) and the Ising cases in the extremely low doping regime, i.e. when asingle hole added to the strongly interacting half-filled system becomes apolaron. We show that in the realistic Ising case the three-site terms play avital role in the polaron movement and should never be neglected unlike in theSU(2) case.

Polaron in the t-J Models with Three-Site Terms: the SU(2) and the Ising Cases