Ordering of geometrically frustrated classical and quantum triangular Ising magnets

Ying Jiang and Thorsten Emig
Phys. Rev. B 73, 104452 – Published 31 March 2006

Abstract

A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. 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. By mapping the Ising models on a triangular lattice to elastic lattices of noncrossing strings, we derive an exact relation between the spin variables and the displacement field of the strings. Using this map for both the classical (2+1)D stacked model and the quantum frustrated 2D system, we obtain a microscopic derivation of an effective Hamiltonian which was proposed before on phenomenological grounds within a Landau-Ginzburg-Wilson approach. In contrast to the latter approach, our derivation provides the coupling constants and hence the entire transverse field-versus-temperature phase diagram can be deduced, including the universality classes of both the quantum and the finite-temperature transitions. The structure of the ordered phase is obtained from a detailed entropy argument. We compare our predictions to recent simulations of the quantum system and find good agreement. We also analyze the connections to a dimer model on the hexagonal lattice and its height profile representation, providing a simple derivation of the continuum free energy and a physical explanation for the universality of the stiffness of the height profile for anisotropic couplings.

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  • Received 29 August 2005

DOI:https://doi.org/10.1103/PhysRevB.73.104452

©2006 American Physical Society

Authors & Affiliations

Ying Jiang and Thorsten Emig

  • Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany

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Issue

Vol. 73, Iss. 10 — 1 March 2006

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