Sign of corrections to scaling amplitudes: Field-theoretic considerations and results for self-repelling walks

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Abstract
I discuss the application of renormalized field theory to such critical systems where the renormalized coupling approaches the fixed point from the ‘‘wrong’’ (strong-coupling) side. In contrast to a belief sometimes expressed in the literature, I find that also this situation can be described within the standard formalism, only the interpretation of the strong-coupling branch relies on the existence of a finite cutoff. I illustrate these considerations with an analysis of Monte Carlo data for self-avoiding walks, finding that the data support the theory in all respects. However, it is stressed that the nonuniversal parameters of the renormalized theory in general have no simple relation to the parameters of the underlying bare model.