Spin Dynamics Tutorial: Numerical Simulations

Derivatives of spin dynamics simulations.

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate, and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation, and stability analysis of s...

Numerical Simulations of Spin Glass Systems

We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few ap...

Numerical Simulations Of Spin Glass Systems

Stochastic Spin Dynamics & Langevin-Landau-Gilbert Simulations

Here I discuss the dynamics of microscopic systems, primarily for spin models, in thermal equilibrium, where the temperature causes random forces or torques, which are in competition with a damping force. This includes summarizing Langevin dynamics and finding methods for integrating the Landau-Gilbert equation of micromagnetics in time, with damping & temperature. The goal is to understand how...

Parallel algorithm for spin and spin-lattice dynamics simulations.

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, Phys. Rev. B 78, 024434 (2008)]. The algorithm is successfully tested in both types of dynamic ...