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We investigate the equivalence of the sine-Gordon and Thirring models on the basis of the short-distance behavior in the massive Thirring model. We find that for dim ψ ψ≥ 1 there is a new additive renormalization effect originating from the occurrence of nonleading mass singularities in the spinor vacuum expectation values. In the sine-Gordon language this effect makes its appearance as a" cumulative" mass effect. It leads to a breakdown of the naive variational method.