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We consider the quantum Heisenberg antiferromagnet in a magnetic field on two one-dimensional lattices containing equilateral triangles (a chain of corner-sharing double tetrahedra and a frustrated three-leg ladder) which support localized-magnon states. By mapping of the localized-magnon degrees of freedom on a classical lattice gas we obtain high-field thermodynamic quantities of the models at low temperatures.

Low-Temperature Properties of the Quantum Heisenberg Antiferromagnet on Some One-Dimensional Lattices Containing Equilateral Triangles