Domino model for geomagnetic field reversals

Abstract

We solve the equations of motion of a one-dimensional planar Heisenberg (or Vaks-Larkin) model consisting of a system of interacting macro-spins aligned along a ring. Each spin has unit length and is described by its angle with respect to the rotational axis. The orientation of the spins can vary in time due to spin-spin interaction and random forcing. We statistically describe the behavior of the sum of all spins for different parameters. The term "domino model" in the title refers to the interaction among the spins.We compare the model results with geomagnetic field reversals and dynamo simulations and find strikingly similar behavior. The aggregate of all spins keeps the same direction for a long time and, once in a while, begins flipping to change the orientation by almost 180 degrees (mimicking a geomagnetic reversal) or to move back to the original direction (mimicking an excursion). Most of the time the spins are aligned or anti-aligned and deviate only slightly with respect to the rotational axis (mimicking the secular variation of the geomagnetic pole with respect to the geographic pole). Reversals are fast compared to the times in between and they occur at random times, both in the model and in the case of the Earth's magnetic field.

Using “domino” model to study the secular variation of the geomagnetic dipolar moment

“…This model was proposed by Mazaud and Laj (1989) and then applied by Mori et al (2013) 6 to study geomagnetic field reversals.…”

Insights into pre-reversal paleosecular variation from stochastic models

“…We considered two variations of macro-spin interactions: macro-spins interacting pair-wise with their neighbors and macro-spin interacting with all other macro-spins. In the first case the coupling is confined in short distances, hence we have the Short-range Coupling Spins FIGURE 1 | Sketch of the Standard "Domino" model (adapted from Mori et al, 2013).…”

“…The numerical models span from models based on magneto-hydrodynamics (MHD) partial differential equations (Rüdiger and Hollerbach, 2004;Christensen and Wicht, 2007) to "toy" models like the "domino" model (Nakamichi et al, 2011;Mori et al, 2013;Duka et al, 2015) or Rikitake two-disk dynamo (Hoshi and Kono, 1988). The time series obtained by numerically simulating various MHD models show that geomagnetic field reversals occur by imposing different conditions and different parameter values on the 3D dynamo equations Roberts, 1995, 1997;Glatzmaier et al, 1999).…”

“…These convective column cells are considered as dynamo cells (elements) and the dynamo mechanism would be a collection of the interactions of such elements (Nakamichi et al, 2011). Inspired by the idea that the convective Taylor column behaves as dynamo cell, Mori et al (2013), proposed a simple model ("domino" model) composed of N macro-spins which are aligned along a ring and interact in a prescribed fashion (Figure 1). In detail, the macro-spins are embedded in a uniformly rotating medium and along the rotational axis lays the unit angular velocity vector = (0; 1).…”

“…Despite their simplicity, "toy" models seem to reproduce quite accurately many features of the geomagnetic field temporal variations. One of these models, the "domino" model, appears with several versions, but two of them are of particular interest: the Shortrange Coupled Spins (SCS) model (Mori et al, 2013) and the Long-range Coupled Spins (LCS) model (Nakamichi et al, 2011;Duka et al, 2015). Another model is the Rikitake model.…”