Some numerical results on the block spin transformation for the 2D Ising model at the critical point

We study the block spin transformation for the 2D Ising model at the critical temperatureT _c . We consider the model with the constraint that the total spin in each block is zero. An old argument by Cassandro and Gallavotti strongly supports the Gibbsianness of the transformed measure, provided that such model has a critical temperatureT _c lower thanT _c . After describing a possible rigorous approach to the problem, we present numerical evidence that indeedT _c <T _c and study the Dobrushin-Shlosman uniqueness condition.