  We study linear functionals on a Clifford algebra (algebra of Ma- joranas)
equipped with a reflection automorphism. For Hamiltonians that are functions of
Majoranas or of spins, we find necessary and sufficient conditions on the
coupling constants for reflection positivity to hold. One can easily check
these conditions in concrete models. We illustrate this by discussing a number
of spin systems with nearest-neighbor and long-range interactions.
