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

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

1998-05-19

arxiv.org/abs/cond-mat/9805223v1

Phys.Rev.E58:2673-2676,1998

Physics

Condensed Matter

Statistical Mechanics

3pages, 2 figures

Scientific paper

10.1103/PhysRevE.58.2673

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.

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