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Title: Parallel algorithm for spin and spin-lattice dynamics simulations
Authors: Ma, PW
Woo, CH 
Issue Date: 6-Apr-2009
Source: Physical review. E, Statistical, nonlinear, and soft matter physics, Apr. 2009, v. 79, no. 4, 046703, p. 1-8
Abstract: To control numerical errors accumulated over tens of millions of time steps during the integration of a set of highly coupled equations of motion is not a trivial task. In this paper, we propose a parallel algorithm for spin dynamics and the newly developed spin-lattice dynamics simulation [ P. W. Ma et al. Phys. Rev. B 78 024434 (2008)]. The algorithm is successfully tested in both types of dynamic calculations involving a million spins. It shows good stability and numerical accuracy over millions of time steps (∼1 ns). The scheme is based on the second-order Suzuki-Trotter decomposition (STD). The usage can avoid numerical energy dissipation despite the trajectory and machine errors. The mathematical base of the symplecticity, for properly decomposed evolution operators, is presented. Due to the noncommutative nature of the spin in the present STD scheme, a unique parallel algorithm is needed. The efficiency and stability are tested. It can attain six to seven times speed up when eight threads are used. The run time per time step is linearly proportional to the system size.
Keywords: Lattice dynamics
Numerical analysis
Spin dynamics
Publisher: American Physical Society
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
ISSN: 1539-3755
EISSN: 1550-2376
DOI: 10.1103/PhysRevE.79.046703
Rights: Physical Review E © 2009 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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