  We study the block spin transformation for the 2D Ising model at the critical
temperature $T_c$. We consider the model with the constraint that the total
spin in each block is zero. An old argument by Cassandro and Gallavotti allows
to show that the Gibbs potential for the transformed measure is well defined,
provided that such model has a critical temperature $T'_c$ lower than $T_c$.
After describing a possible rigorous approach to the problem, we present
numerical evidence that indeed $T'_c<T_c$, and a study of the
Dobrushin-Shlosman uniqueness condition.
