Elucidation of Ground-State Spin Configurations of Ising Models in a Magnetic Field with Frustration on a Diamond Hierarchical Lattice

To study the ground-state spin configuration as a function of magnetic field, the spin configurations at each stage lattice are determined by analyzing recursion equations. The exact calculation of the magnetization curve by Hirose et al. [J. Phys. Soc. Jpn. 83, 074716 (2014)] shows that an infinitely small applied magnetic field on the zero-field classical spin-liquid phase can induce an infinitely small magnetization, which is as if this Ising system has a gapless spectrum. In this study, we reveal that an infinitely small applied field makes a large number of spins flip upwards with the exchange-energy loss remaining finite. This exotic behavior originates from the frustration effect of diamond structures and an inherent long-range nature of hierarchical lattices.