Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice

TL;DR

This paper provides exact solutions for the ground states of frustrated Ising models on diamond hierarchical lattices, revealing unique magnetization behaviors and the influence of lattice structure on magnetic properties.

Contribution

It presents exact ground state solutions and analyzes magnetization phenomena in frustrated Ising models on hierarchical lattices, highlighting the effects of frustration and lattice topology.

Findings

Magnetization cannot saturate under finite magnetic fields due to frustration.

Infinitesimal magnetic fields induce infinitesimal magnetization in the spin-liquid phase.

The structure of the partition function explains the gapless-like behavior.

Abstract

Magnetization processes of Ising models with frustration on diamond hierarchical lattices, which contain vertices with high coordination numbers, are exactly obtained at zero temperature. In antiferromagnetic systems, the magnetization cannot saturate under finite magnetic fields owing to the competition between the antiferromagnetic and Zeeman interactions and the intrinsic long-range nature of hierarchical lattices. For the zero-field classical spin-liquid phase found in [Kobayashi et al., J. Phys. Soc. Jpn. 78, 074004 (2009)], an infinitely small applied magnetic field can induce an infinitely small magnetization, despite Ising models that have discrete energy levels. By examining the structure of the partition function, we obtain the ground state spin-configurations and clarify the mechanism of the "gapless like behavior".