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The influence of long-range interactions decaying in d dimensions as1/R^{d+\sigma} on the critical behavior of systems with Fisher'scorrelation-function exponent for short-range interactions \eta_{SR}<0, isre-examined. Such systems, typically described by \Phi ^{3}-field theories, aree.g. the Potts-model in the percolation-limit, the Edwards-Anderson spin-glass,and the Yang-Lee edge singularity. In contrast to preceding studies, it isshown by means of Wilson's momentum-shell renormalization-group recursionrelations that the long-range interactions dominate as long as \sigma <2-\eta_{SR}. Exponents change continuously to their short-range values at theboundary of this region.Comment: 3pages, 2 figure

Influence of Long-range Interactions on the Critical Behavior of Systems with negative Fisher-Exponent