Abstract
We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, and , respectively, in the presence of a magnetic field appropriately tuned. We find that when the pair interaction dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction dominates, the boundaries between the two cases being at . 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 () 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 and temperatures , the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction .
7 More- Received 24 February 2022
- Accepted 4 July 2022
DOI:https://doi.org/10.1103/PhysRevE.106.014149
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