Triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferro magnet on a triangular lattice in the presence of a staggered field conjuga te to one of the degenerate ground states. Using a mapping of the ground st ates of the model without the staggered field to dimer coverings on the dua l lattice, we classify the ground states into sectors specified by the numb er of "strings." We show that the effect of the staggered field is to gener ate long-range interactions between strings. In the limiting case of the an tiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower b ound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three differen t dynamics. We find that in all the three cases, equilibration times for lo w-field values increase rapidly with system size at low temperatures. Due t o this difficulty in equilibrating sufficiently large systems at low temper atures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of st phase transition for finite values of J. A surprising feature in the system is the fact that un like usual glassy systems; a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.