Frustration in a generalized kagomé Ising antiferromagnet: Exact results

K. A. Muttalib and J. H. Barry
Phys. Rev. E 106, 014149 – Published 29 July 2022

Abstract

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, J2 and J3, respectively, in the presence of a magnetic field h appropriately tuned. We find that when the pair interaction J2<0 dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction J3 dominates, the boundaries between the two cases being at J3=±J2. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter (J2<0) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields h and temperatures T, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact T=0 threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction J3.

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  • Received 24 February 2022
  • Accepted 4 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.014149

©2022 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

K. A. Muttalib and J. H. Barry

  • Department of Physics, University of Florida, P.O. Box 118440, Gainesville, Florida 32611-8440, USA

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Issue

Vol. 106, Iss. 1 — July 2022

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