Geometric integrators for classical spin systems

Journal of Computational Physics

Volumn 133, Issue 1, 1997, Pages 160-172

  Frank, Jason ^a   Huang, Weizhang ^b   Leimkuhler, Benedict ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF KANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HAMILTONIANS; SPIN DYNAMICS;

CLASSICAL SPIN; GEOMETRIC INTEGRATORS; HEISENBERG SPIN SYSTEMS; RED-BLACK; SPIN SYSTEMS; SPIN-S SYSTEMS; SPLITTINGS; STRUCTURE-PRESERVING; SYMMETRIC ENERGY; TIME-STEPPING SCHEMES;

RUNGE KUTTA METHODS;

EID: 0031139085     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5672     Document Type: Article

References (24)

1. Wisdom J., Holman M. Astron. J. 102:1991;1528.
2. Marsden J. E. Lectures on Mechanics. 1992;Cambridge Univ. Press, Cambridge.
3. A. Bloch, P. S. Krishnaprasad, J. E. Marsden, T. Ratiu, 1996, The Euler-Poincaré equations and double bracket dissipation.
4. Cooper G. IMA J. Numer. Anal. 7:1987;1.
5. Dichmann D. J., Maddocks J. H. J. Nonlinear Sci. 6:1996;271.
6. Faddeev L. D., Takhtajan L. A. Hamiltonian Methods in the Theory of Solitons. 1987;Springer-Verlag, Berlin.
7. O. Gonzales, J. Simo, Comput. Methods Appl. Mech. Engrg.
8. B. Leimkuhler, G. Patrick, J. Nonlinear Sci.
9. Leimkuhler B., Reich S. Math. Comput. 63:1994;589.
10. McLachlan R. Numer. Math. 66:1994;465.
11. F. G. Mertens, G. M. Wysin, A. R. Völkel, A. R. Bishop, H. J. Schnitzer, 1993, Cyclotron-like oscillations and boundary effects in the 2-vortex dynamics of easy-plane magnets, Bayreuth Workshop on Nonlinear Coherent Structures.
12. Olver P. J. Applications of Lie Groups to Differential Equations. 1986;Springer-Verlag, New York.
13. Papanicolaou N., Zakrewski W. J. Physica D Nonlinear Phenomena. 80:1995;225.
14. Reich S. Physica D. 76:1994;375.
15. J. A. G. Roberts, C. J. Thompson, 1987, Dynamics of the Classical Heisenberg Spin Chain, Mathematics Department, University of Melbourne, Parkville, Victoria, 3052, Australia.
16. Frutos J., Ortega T., Sanz-Serna J. M. Comput. Method. Appl. Mech. Engrg. 80:1990;417.
17. Sanz-Serna J. M., Calvo M. P. Numerical Hamiltonian Problems. Applied Mathematics and Mathematical Computation. 7:1994;Chapman and Hall, London.
18. Sun G. J. Comput. Math. 11:1993;365.
19. Takhtajan L. A. Phys. Lett. A. 64:1977;235.
20. Völkel A. R., Mertens F. G., Bishop A. R., Wysin G. M. Phys. Rev. B. 43:1991;5992.
21. A. R. Völkel, F. G. Mertens, G. M. Wysin, A. R. Bishop, H. J. Schnitzer, 1993, Collective variable approach for a magneticN, Bayreuth Workshop on Nonlinear Coherent Structures.
22. Wysin G. M. Phys. Rev. B. 49:1994;8780.
23. G. M. Wysin, F. G. Mertens, A. R. Völkel, A. R. Bishop, 1993, Mass and momentum for vortices in two-dimensional easy-plane magnets, Bayreuth Workshop on Nonlinear Coherent Structures.
24. Yoshida H. Phys. Lett. A. 150:1990;262.