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

H. K. Janssen
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Abstract

The influence of long-range interactions decaying in d dimensions as 1/R^{d+σ} on the critical behavior of systems with Fisher's correlation-function exponent for short-range interactions η_{SR}<0, is re-examined. Such systems, typically described by Φ^{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 σ<2-η_{SR}. Exponents change continuously to their short-range values at the boundary of this region.

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H. K. Janssen. 1998-05-19. Influence of Long-range Interactions on the Critical Behavior of Systems with negative Fisher-Exponent. https://doi.org/10.1103/physreve.58.2673

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