  Fermion systems in discrete space-time are introduced as a model for physics
on the Planck scale. We set up a variational principle which describes a
non-local interaction of all fermions. This variational principle is symmetric
under permutations of the discrete space-time points. We explain how for
minimizers of the variational principle, the fermions spontaneously break this
permutation symmetry and induce on space-time a discrete causal structure.
