Geometric integrators for classical spin systems
type: Item
instance of: scholarly article
title: Geometric integrators for classical spin systems
zbMATH Open document ID: 0878.65110
author: Jason Frank
author: Weizhang Huang
author: Benedict Leimkuhler
published in: Journal of Computational Physics
publication date: 1998-01-12T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/11554
review text: Practical, structure preserving methods for integrating classical Heisenberg spin systems are discussed. One of the new integrators, the Lie-Poisson method, is derived based upon a Hamiltonian splitting: it conserves all of the integrals (spin-length and total spin) of the differential equations but the energy. The other integrator is derived based upon a red-black splitting and staggered time stepping. This method is time symmetric and conserves all the available first integrals.The methods are applied to the one- and two-dimensional lattice models and are compared with the commonly used explicit Runge-Kutta, projected Runge-Kutta, and implicit mid point schemes on the basis of accuracy, conservation of invariants and computational expense.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81V45
Mathematics Subject Classification ID: 82C20
zbMATH DE Number: 1036498
zbMATH Keywords: Heisenberg spin systems
zbMATH Keywords: lattice models
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: Landau-Lifshitz equation
zbMATH Keywords: Lie-Poisson method
zbMATH Keywords: Hamiltonian splitting
zbMATH Keywords: red-black splitting
zbMATH Keywords: time stepping
MaRDI profile type: Publication
OpenAlex ID: W2007293127
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DOI: 10.1006/JCPH.1997.5672
description: scientific article; zbMATH DE number 1036498