N. Mori, D. Schmitt, A. Ferriz-Mas, J. Wicht, H. Mouri, A. Nakamichi, M. Morikawa
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 random forcing and spin-spin interaction. We statistically describe the
behaviour 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 find
strikingly similar behaviour. 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.
View original:
http://arxiv.org/abs/1110.5062
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