Journal of Statistical Physics, Vol. 58, Nos. 1/2, 1990. p. 141-157.
We introduce a lattice gas for particles with discrete momenta (1, 0, -1) and local deterministic microdynamics, which exactly reproduces Creutz's micro-canonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.