  The influence of long-range interactions decaying in d dimensions as
1/R^{d+\sigma} on the critical behavior of systems with Fisher's
correlation-function exponent for short-range interactions \eta_{SR}<0, is
re-examined. Such systems, typically described by \Phi ^{3}-field theories, are
e.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 is
shown by means of Wilson's momentum-shell renormalization-group recursion
relations that the long-range interactions dominate as long as \sigma <2-\eta
_{SR}. Exponents change continuously to their short-range values at the
boundary of this region.
