We apply renormalization-group methods to study the density of Yang-Lee zeros at the edges of the gap in Ising systems with correlated random-$T_c$ impurities. The impurity correlations are assumed to fall off at large distances as ∼$R^{\mathrm{-}\left(d\mathrm{-}\theta \right)}$ (θ>0). Both short- and long-range spin interactions decaying as ∼$R^{\mathrm{-}(d+\sigma )}$ (0<σ<2) are considered. We find that the edge singularities are described by a new fixed point in the underlying ${\phi }^3$-field model with imaginary coupling and imaginary correlated random fields. We obtain the edge exponents to leading order in the ε̃ expansion, where ε̃=$d_c$-d with $d_c$=8+θ for short- and $d_c$=4σ+θ for long-range interactions which do not obey any apparent dimensional reduction rule.

• Received 25 June 1987

DOI:https://doi.org/10.1103/PhysRevB.37.3569