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

TL;DR

This paper investigates how long-range interactions affect the critical behavior of certain systems with negative Fisher's exponent, revealing that these interactions dominate under specific conditions and cause continuous changes in critical exponents.

Contribution

It provides a re-examination using Wilson's renormalization-group approach, showing the dominance of long-range interactions for systems with negative ta_{SR} and identifying the boundary where exponents revert to short-range values.

Findings

Long-range interactions dominate when ta_{SR}<0 and rac{\sigma}{2-ta_{SR}}.

Critical exponents change continuously at the boundary rac{\sigma}{2-ta_{SR}}=1.

The study applies to models like the Potts model, spin glasses, and Yang-Lee edge singularity.

Abstract

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.