The edge of the gap in the distribution of Yang-Lee zeros at $H=i{H}_0\mathrm{}\left(T\right)\mathrm{}$ on the imaginary magnetic field axis in ferromagnets above $T_c$ is essentially a critical point. In terms of the edge exponents $\delta$ and $\eta$, the density of zeros obeys $\mathcal{G}\left(H^{\prime \prime }\right)\sim {[H^{\prime \prime }-H_0\mathrm{}(T\left)\right]}^{\sigma }$, with $\sigma =\frac{1}{\delta }=\frac{(d-2+\eta )}{(d_2-\eta )}$. Classical behavior ($\sigma =\frac{1}{2}$) occurs for $d>\mathrm{}{d}^{\times }=6\mathrm{}$. The appropriate field-theoretic renormalization group entails a $w{\varphi }^3$ coupling and, with $\epsilon =6-d>~0$, yields $\eta \approx -\frac{\epsilon }{9}$ for all $n<\mathrm{}\infty$. This correlates well with refined series estimates for $d=2\mathrm{}$ and $d=3\mathrm{}$ and with exact results for $d=1\mathrm{}$ ($\eta =-1\mathrm{}$).

• Received 20 April 1978

DOI:https://doi.org/10.1103/PhysRevLett.40.1610