Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice

We have studied the compressible antiferromagnetic Ising Model on a triangular lattice using Monte Carlo simulations. It is found that the coupling to the strain removes the frustration of the rigid model and the simulations show a transition from the disordered to an ordered, striped phase at low temperatures. This transition involves two broken symmetries: the Ising symmetry and a three-state Potts symmetry characteristic of the triangular lattice. In the absence of bond fluctuations, this transition is always strongly first order. Using finite-size scaling analysis, we find evidence that, in the presence of fluctuations, the transition becomes weakly first order and possibly second order when the coupling to the lattice is increased. We discuss the relevance of this model to certain phase transitions in alloys.