Nonperturbative nature of the renormalization group

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Abstract
By considering Symanzik’s improvement program of the continuum limit of scalar lattice field theory as a tool to make contact between the perturbative renormalization and Wilson’s theory, we show the nonperturbative nature of the renormalization. As a consequence we justify the conjecture of Parisi that the critical exponents may be estimated by field-theoretical methods without recourse to the ε expansion.