Influence of Long-range Interactions on the Critical Behavior of Systems with negative Fisher-Exponent
H. K. Janssen
Abstract
The influence of long-range interactions decaying in d dimensions as 1/Rd+σ on the critical behavior of systems with Fisher's correlation-function exponent for short-range interactions ηSR<0, is re-examined. Such systems, typically described by Φ3-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 σ<2-ηSR. Exponents change continuously to their short-range values at the boundary of this region.
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