Now we consider a certain blocking transformation of the state variables { s i } → → { s ~ ~ i } , the number of s ~ ~ i must be lower than the number of s i . Now let us try to rewrite the Z function only in terms of the s ~ ~ i . If this is achievable by a certain change in the parameters, { J k } → → { J ~ ~ k } , then the theory is said to be renormalizable. The most important information in the RG flow are its fixed points. The possible macroscopic states of the system, at a large scale, are given by this set of fixed points. If these fixed points correspond to a free field theory, the theory is said to be trivial. Numerous fixed points appear in the study of lattice Higgs theories, but the nature of the quantum field theories associated with these remains an open question.