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We study the block spin transformation for the 2D Ising model at the criticaltemperature $T_c$. We consider the model with the constraint that the totalspin in each block is zero. An old argument by Cassandro and Gallavotti allowsto 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 presentnumerical evidence that indeed $T'_c<T_c$, and a study of theDobrushin-Shlosman uniqueness condition.Comment: 34 pages including figures added as uufile. ROMA repor

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