An Ising antiferromagnet on a stacked triangular lattice in zero field is studied by Monte Carlo simulations, focusing on the character of the low-temperature phase and the effect of the relative strength of the exchange interaction in the stacking direction α. Our results support the presence of the 3D Wannier phase, with the sublattice magnetization structure (m, -m, 0) and power-law decaying m with the lattice size. The extent of this low-temperature phase shrinks with decreasing α, however, it appears even at very low values if it is accessed from higher temperatures by sufficiently slow cooling.
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