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 c ritical temperature T-c. We consider the model with the constraint tha t the total spin in each block is zero. An old argument by Cassandro a nd Gallavotti strongly supports the Gibbsianness of the transformed me asure, provided that such model has a critical temperature T'(c) lower than T-c. After describing a possible rigorous approach to the proble m, we present numerical evidence that indeed T'(c) < T-c and study the Dobrushin-Shlosman uniqueness condition.