Exotic phases in geometrically frustrated triangular Ising magnets

We report a systematic study of both quantum and classical geometrically frustrated Ising models with competing ordering mechanism. The ordering comes in the classical case from a coupling of two-dimensional (2D) layers and in the quantum model from the quantum dynamics induced by a transverse field. We develop a microscopic derivation of the Landau–Ginzburg–Wilson (LGW) Hamiltonian for these models and show that it can be interpreted as the free energy of three-dimensional (3D) elastic non-crossing strings. By utilizing this effective Hamiltonian, the entire transverse field versus temperature phase diagram for the 2D quantum Ising model is obtained analytically, including the universality classes of both the quantum and the finite temperature transitions. The structures of the ordered phases in both 3D classical and 2D quantum Ising models are obtained from a detailed entropy argument. The results are in excellent agreement with recent numerical simulations. The competition of quantum and thermal fluctuations is crucial in finding and understanding exotic phases in geometrically frustrated magnets [1, 2]. For geometrically frustrated Ising system, the macroscopic degeneracy of the classical ground state may endow the system with a continuous symmetry which precludes an ordered phase at finite temperatures for 2D quantum magnets due to the Mermin–Wagner theorem [3]. Another possible but contrary scenario is ‘order-from-disorder’ [4] where quantum fluctuations select a small particularly susceptible class of the ground-state manifold and yield an ordered symmetry-broken state [5]. Hence one expects that weak competing fluctuations about the classical ground states is able to generate new strongly correlated states and phase transitions of unexpected universality classes. The antiferromagnetic Ising model on a triangular lattice (TIAF) H = J ∑