Geomagnetism is extremely complex and straightforward magnetohydrodynamics simulations are still unable to reveal all its dynamics. Recently, a simple macro-spin model for geomagnetism has been suggested. This model is based on the idea that geomagnetism can be described by interactions with many local dynamo elements (macro-spins). This model can reproduce some complex features of geomagnetism by solving a simple set of ordinary differential equations with a minimal number of variables. In this paper, we complete this macro-spin model by considering the full set of variables in three dimensions. Utilizing this model, we can address several basic features of geomagnetism which could not be described in the previous minimal model: migration of the north and south magnetic poles, a precise comparison of the detailed surface distribution of magnetic fields with the observed data, etc. Moreover, by applying this model to solar magnetism, we can reproduce the periodic polarity reversals and the power index of the power spectrum from this complete spin model. Finally, we elucidate the statistical properties of pole migration.

中文翻译：

---

具有两个变量的耦合宏观自旋模型，用于地球和太阳的极性反转

地磁是极其复杂的，直接的磁流体动力学模拟仍然无法揭示其所有动力学。最近，有人提出了一种简单的地磁宏观自旋模型。该模型基于这样的想法，即地磁可以通过与许多局部发电机元素（宏观旋转）的相互作用来描述。该模型通过求解一组具有最少变量的简单常微分方程，可以再现地磁的一些复杂特征。在本文中，我们通过考虑三个维度的全套变量来完成这个宏观自旋模型。利用这个模型，我们可以解决以前最小模型中无法描述的地磁的几个基本特征：南北磁极的迁移，将磁场的详细表面分布与观测数据等进行精确比较。此外，通过将该模型应用于太阳磁学，我们可以从这个完整的自旋模型再现周期性极性反转和功率谱的功率指数。最后，我们阐明了极点迁移的统计特性。