Critical Behavior of Branched Polymers and the Lee-Yang Edge Singularity

The exponents for large branched dilute polymers (which are also connected with the exponents of the lattice animals) are related in $D$ dimensions to the exponents of the Lee-Yang edge singularity of the Ising model in $D\ensuremath{-}2$ dimensions. From the exact solution of the Ising model in zero and one dimension, one gets the polymer exponents in two and three dimensions, $\ensuremath{\theta}(D=2)=1$ and $\ensuremath{\theta}(D=3)=\frac{3}{2}$.