Emergent Potts Z3 order in the Heisenberg windmill model with biquadratic exchange interactions*

We design and study a bilinear-biquadratic Heisenberg model with coexisting ferro- and antiferromagnetic exchange interactions on the windmill lattice, which consists of coupled triangular and honeycomb lattices. Spins on the triangular layer are coupled antiferromagnetically, while spins on the honeycomb layer interact ferromagnetically. We determine the classical ground state phase diagram, which includes a variety of phases including a non-coplanar canted umbrella state, canted coplanar phases and a fully ferromagnetic state, resembling the finite-temperature finite-magnetic field phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice. We identify a region in the classical ground state phase diagram with a Z3-degenerate ground state. Using Monte-Carlo simulations and analytical techniques, we determine the finite-temperature phase diagram above this phase and identify a finite-temperature Potts phase transition of an emergent Z3 order parameter.