  We study spin tunnelling in molecular magnets as an instance of a mesoscopic
phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel
splitting between various pairs of Zeeman levels in this molecule oscillates as
a function of applied magnetic field, vanishing completely at special points in
the space of magnetic fields, known as diabolical points. This phenomena is
explained in terms of two approaches, one based on spin-coherent-state path
integrals, and the other on a generalization of the phase integral (or WKB)
method to difference equations. Explicit formulas for the diabolical points are
obtained for a model Hamiltonian.
