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.

27 pages, 9 figures

References in corpus (1)

• Fractional magnetization plateaus and magnetic order in the Shastry Sutherland magnet TmB4

Cited by in corpus (4)

• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• 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