Finite size effects at the Yang-Lee edge singularity and branched polymers in a plate geometry

Finite size scaling effects are investigated for Ising-like systems in a hypercube Ld near the Yang-Lee edge singularity. Besides exact results for d = 1, we present series in ε13 for some universal quantities in dimensions d = 6 − ε gained by field-theoretic techniques. Using the supersymmetric connection between the Yang-Lee theory in dimension d and the statistics of branched polymers in D = d + 2, we find the animal number in a periodic plate geometry with 2 infinite and d compactified dimensions. In particular, we exactly calculate the full cross-over between three-dimensional and two-dimensional animals.