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

TL;DR

This paper provides exact zero-temperature magnetization calculations for frustrated ferro- and antiferromagnetic Ising models on diamond hierarchical lattices, revealing infinite magnetization steps and unique responses to small magnetic fields.

Contribution

It presents the first exact analysis of magnetization steps in frustrated Ising models on hierarchical lattices, highlighting phenomena absent in simpler models.

Findings

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

Magnetization cannot saturate in antiferromagnetic systems under finite fields.

Hierarchical lattice structure influences long-range magnetic behavior.

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.