  The dynamics of a physical system is linked to its phase-space geometry by
Noether's theorem, which holds under standard hypotheses including continuity.
Does an analogous theorem hold for discrete systems? As a testbed, we take the
Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show
that---and why---energy not only acts as a generator of the dynamics for this
family of systems, but is also conserved when the dynamics is time-invariant.
