On classical models of Spin

Mirjana Božić, Z. Marić

Joshua J. Heiner, David R. Thayer

A nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a classically driven nonlinear differential equation with dissipation and a semi-classical interpretation of the torque on a spin magnetic moment in the presence of a realistic magnetic field, which will represent two equilibrium positions. The highly complicated driven nonlinear dissipative semi-classical model is used to introduce chaos, which is necessary to produce the correct statistical quantum results. The resemblance between this semi-classical spin model and the thoroughly studied classical driven-damped nonlinear pendulum are shown and discussed.

Gemma De las Cuevas, Toby S. Cubitt

Spin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain "universal models," with at most polynomial overhead. This holds for classical models with discrete or continuous degrees of freedom. We prove necessary and sufficient conditions for a spin model to be universal and show that one of the simplest and most widely studied spin models, the two-dimensional Ising model with fields, is universal. Our results may facilitate physical simulations of Hamiltonians with complex interactions.

Andreas Wipf

Meng Wen, Heiko Bauke, Christoph H. Keitel

Different classical models have been proposed to describe the dynamics of electrons including their spin degree of freedom by coupled equations for the orbital motion and spin precession. Two representative models with spin-dependent forces which originate from a classical limit of quantum mechanics and from purely classical considerations are compared exemplarily and benchmarked to the quantum dynamics as predicted by the Dirac equation. We demonstrate that different models can lead to different or even contradicting predictions how the spin degree of freedom modifies the electron's orbital motion, when an electron moves in strong electromagnetic fields. In this way, one may evaluate the validity and identify the limits of these classical models via a comparison with possible experiments to provide a suitable description of spin-induced dynamics for applications in many-particle systems.

Fabián H. Gaioli, Edgardo T. Garcia Alvarez