The triangular Ising antiferromagnet in a staggered field

TL;DR

This study investigates the equilibrium behavior of a triangular lattice Ising antiferromagnet under a staggered field, revealing long-range interactions, phase transition evidence at infinite coupling, and complex low-temperature dynamics.

Contribution

It introduces a mapping to dimer coverings, classifies ground states by string sectors, and proves a phase transition at infinite coupling, providing new insights into the model's phase behavior.

Findings

Long-range interactions between strings induced by the staggered field

Existence of a phase transition at infinite coupling with a finite lower bound for transition temperature

Equilibration times grow rapidly at low temperatures, complicating finite-size scaling analysis

Abstract

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of ``strings''. We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems, a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.