Some exchange kinetics are introduced into the antiferromagnetic Ising model on a triangular lattice. These connect the degenerate ground-states and give rise to a set of random walks over the resulting irregular network in the phase space. Some theoretical analysis of the elementary processes is presented together with the results of a related Monte Carlo experiment. Some features of the system are found suggestive of a liquid-glass transition, although we have not yet conclusively demonstrated the existence of such a transition in this system. An approximate ground-state energy is also evaluated for the antiferromagnetic Heisenberg model on a triangular lattice.