Yang-Lee Edge Singularity and ϕ3 Field Theory

The edge of the gap in the distribution of Yang-Lee zeros at H=iH₀(T) on the imaginary magnetic field axis in ferromagnets above T_c is essentially a critical point. In terms of the edge exponents δ and η, the density of zeros obeys G(H'')~[H''-H₀(T)]^σ, with σ=1δ=(d-2+η)(d₂-η). Classical behavior (σ=12) occurs for d>d^×=6. The appropriate field-theoretic renormalization group entails a wϕ³ coupling and, with ɛ=6-d>=0, yields η~-ɛ9 for all n<∞. This correlates well with refined series estimates for d=2 and d=3 and with exact results for d=1 (η=-1).