EDIT: But Alex wants deterministic time evolution, which basically means either you have a quantum Ising model (which maybe should count as continuous state space even though the physical space is discrete), or you have a classical Ising model at T=0. Which is maybe not so interesting for the Ising model per se, but there are plenty of classical models of parametric phase transitions at T=0.
You are not going crazy.
EDIT: But Alex wants deterministic time evolution, which basically means either you have a quantum Ising model (which maybe should count as continuous state space even though the physical space is discrete), or you have a classical Ising model at T=0. Which is maybe not so interesting for the Ising model per se, but there are plenty of classical models of parametric phase transitions at T=0.