  In order to prepare for the introduction of dynamical many-body and,
eventually, field theoretical models, we show here that quantum mechanical
exchange interactions in a three-spin chain can emerge from the deterministic
dynamics of three classical Ising spins. States of the latter form an
ontological basis, which will be discussed with reference to the ontology
proposed in the Cellular Automaton Interpretation of Quantum Mechanics by 't
Hooft. Our result illustrates a new Baker-Campbell-Hausdorff formula with
terminating series expansion.
