Infinitely Multiple Steps in Magnetization of Ferro- and Antiferromagnetic Ising Models with Frustration on a Diamond Hierarchical Lattice

Abstract

Magnetizations of ferro- and antiferromagnetic Ising models with frustration on diamond hierarchical lattices are exactly obtained at zero temperature. For the zero-field classical spin-liquid phase found in [Kobayashi {\it et al}, J. Phys. Soc. Jpn. 78, 074004 (2009) ], for which frustrating interactions play an important role, an infinitely small applied magnetic field can induce an infinitely small magnetization, despite classical Ising models that have discrete energy levels. In antiferromagnetic systems, the magnetization cannot saturate under finite magnetic fields owing to the competition between the unfrustrating antiferromagnetic interaction and the Zeeman interaction and an intrinsic long-range nature of hierarchical lattices.

arXiv comment27 pages, 9 figures

References in corpus (5)

• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• Fractional magnetization plateaus and magnetic order in the Shastry Sutherland magnet TmB4
• Magnetization Plateaus in the Shastry-Sutherland Model for SrCu_2(BO_3)_2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation
• Quantum phases in a doped Mott insulator on the Shastry-Sutherland lattice
• Frustrated Ising Model on a Diamond Hierarchical Lattice

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• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Devil's Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions
• Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model from Renormalization-Group Theory
• Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like Decorated Square Lattice
• Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice