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Symplectic integrators for spin systems

Journal article
Authors R. I. McLachlan
Klas Modin
O. Verdier
Published in Physical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume 89
Issue 6
Pages artikel nr 061301
ISSN 1539-3755
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages artikel nr 061301
Language en
Subject categories Mathematical physics


We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R-3. Unlike splittingmethods, it is defined for all Hamiltonians and is O(3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top.

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