  Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg
model are discussed. The adiabatic processes are assumed to consist in the slow
variation of the strength of the magnetic field that environs the spin-systems.
These processes are of current interest in the treatment of cold atoms in
optical lattices and in Adiabatic Quantum Computation. We determine the
probability that, during an adiabatic passage starting from the ground state,
states with higher energy are excited.
