Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment

In an extensive computational experiment, we test Polyakovs conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin $text{U(1)}$ order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling, we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type and at lower temperatures, we find long-range $mathbb{Z}_6$ order.