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Use of potentials in the study of magnet models of the Heisenberg type

Author

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  • Leo, R.A.
  • Mancarella, G.
  • Soliani, G.
  • Solombrino, L.

Abstract

We show that a pair of coupled nonlinear evolution equations can be associated with an extended form of the continuous Heisenberg magnet model. Applying a prolongation technique to these equations, we derive a potential function in terms of which the original system can be expressed. Using the invariance property under the Möbius group of a certain differential equation involving the potential function, we outline a method to get new solutions of the spin system in the extended form starting from trivial ones. As a special application of our machinery, a few examples of solutions of the SU(1,1) magnet model are presented.

Suggested Citation

  • Leo, R.A. & Mancarella, G. & Soliani, G. & Solombrino, L., 1989. "Use of potentials in the study of magnet models of the Heisenberg type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 162(1), pages 67-87.
    • Handle: RePEc:eee:phsmap:v:162:y:1989:i:1:p:67-87
    DOI: 10.1016/0378-4371(89)90556-6
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