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

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

2003-03-22

arxiv.org/abs/cond-mat/0303479v1

Phys. Lett. A 279 (2001) 33-37

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/S0375-9601(00)00811-2

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).

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