Redundant operators for Ising spins

We remind the reader of the important role that could be played in Monte Carlo renormalization-group studies by redundant operators, defined to be changes in the Hamiltonian due to infinitesimal changes of variables. We then overcome the problem of defining an infinitesimal change of variables for discrete Ising spins and construct redundant operators in d=2 and 3. We analyze how they may be seen in numerical experiments.