Finite cutoff and higher transient effects on critical behavior

We recall that, in the study of critical phenomena, the discrete nature of the lattice (finite-cutoff effects) necessitates considering an infinite set of couplings in Wilson's Hamiltonian. This is particularly important for quantities, like the specific heat, which crucially depend on all scales of fluctuations between the lattice spacing and the correlation length and not only on large scales. As a consequence, by taking a precocious infinite-cutoff limit in the renormalization-group equations, one reaches erroneous results.