Classical ground states of spin lattices

Abstract We present a generalization of the Luttinger–Tisza–Lyons–Kaplan theory of classical ground states of Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists of adding certain Lagrange parameters to the diagonal of the Fourier transformed coupling matrix analogous to t...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2022-11, Vol.55 (46), p.465005
Main Authors: Schmidt, Heinz-Jürgen, Richter, Johannes
Format: Article
Language:English
Subjects:
classical spin lattices
ground states
incommensurable ground states
Luttinger–Tisza theory
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Summary:Abstract We present a generalization of the Luttinger–Tisza–Lyons–Kaplan theory of classical ground states of Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists of adding certain Lagrange parameters to the diagonal of the Fourier transformed coupling matrix analogous to the theory of the general ground state problem already published. This approach is illustrated by an application to a modified honeycomb lattice, which has exclusive three-dimensional ground states as well as a classical spin-liquid ground state for different values of the two coupling constants. Another example, the modified square lattice, shows that we can also obtain so-called incommensurable ground states by our method.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aca36d