A long-wave action of spin Hamiltonians and the inverse problem of the calculus of variations

We suggest a method of derivation of the long-wave action of the model spin Hamiltonians using the non-linear partial differential equations of motions of the individual spins. According to the Vainberg's theorem the set of these equations are (formal) potential if the symmetry analysis for the...

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Bibliographic Details
Published inarXiv.org
Main Authors Bostrem, I G, Ovchinnikov, A S, Egorov, R F
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.03.2003
Subjects
Calculus of variations
Ferromagnetism
Inverse problems
Nonlinear differential equations
Nonlinear equations
Partial differential equations
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Summary:We suggest a method of derivation of the long-wave action of the model spin Hamiltonians using the non-linear partial differential equations of motions of the individual spins. According to the Vainberg's theorem the set of these equations are (formal) potential if the symmetry analysis for the Frechet derivatives of the system is true. The case of Heisenberg (anti)ferromagnets is considered. It is shown the functional whose stationary points are described by the equations coincides with the long-wave action and includes the non-trivial topological term (Berry phase).
ISSN:2331-8422
DOI:10.48550/arxiv.0303479