Simulation of geomagnetic reversals through magnetic critical models

Dias, Vitor H. A.; Franco, Jorge O. O.; Papa, Andrés R. R.

doi:10.1590/s0103-97332008000100004

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…Ising-like models have been used in molecular dynamics and statistical mechanics for describing, for instance, phase transitions in ferromagnetism, for modelling spin glasses and for pattern recognition in neural networks [e.g., 26]. Coupled spin models of Ising type, where the individual spins can assume two scalar states +1 or −1 and interact with each other after certain rules, have also been suggested for describing geomagnetic polarity reversals and their statistics [27][28][29]. We analyze a planar Heisenberg model consisting of a system of vectorial spins aligned along a ring.…”

Section: Introductionmentioning

confidence: 99%

Domino model for geomagnetic field reversals

et al. 2013

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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.

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Section: Introductionmentioning

confidence: 99%

Domino model for geomagnetic field reversals

et al. 2013

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“…Before our study, there were some works (Mazaud & Laj 1989; Seki & Ito 1993; Dias, Franco & Papa 2008) in which the spin models with the interaction were studied to reveal the polarity flip dynamics of geomagnetism. They are based on the two‐dimensional Ising model and have found the polarity flip near the critical temperature.…”

Section: Coupled Local Elementsmentioning

confidence: 99%

Coupled spin models for magnetic variation of planets and stars

Nakamichi

Mouri²,

Schmitt

et al. 2012

Monthly Notices of the Royal Astronomical Society

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Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro‐spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many local elements. In this paper, we further develop this idea and construct the minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods etc. This model is characterized by two coexisting phases of spins: i.e. the cluster phase which determines the global dipole magnetic moment, and the expanded phase which gives random perpetual perturbations that yield the intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillations. This corresponds to the case of our Sun and the model well describes the quasi‐regular cycles of the solar magnetism. Furthermore, by analysing the relevant terms of magnetohydrodynamic equations based on our model, we have obtained a scaling relation for the magnetism for planets, satellites and the Sun. Comparing it with various observations, we can estimate the relevant scale of the macro‐spins.

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“…In that model, each spin was supposed to be one ring current in the Earth dynamo and the magnetization was supposed to be proportional to the field intensity. The temperature was used as a tuning parameter [8]. Ising-like models have been used in molecular dynamics and statistical mechanics for describing, phase transitions in ferromagnetism, or for modeling spin glasses [9].…”

Section: Introductionmentioning

confidence: 99%

Possible Causes of Change in the Direction of Earth's Magnetic Field

Gak

Nježić

Škrgić

et al. 2016

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The study of the magnetic properties of materials have attracted the interest of scientists for ages. Knowing the magnetic properties of materials do their best possible use in industry and technology, as well as better understanding of some yet unexplained phenomena in nature related to the Earth's magnetic field. Several models that describe the given phenomenon are known, such as the domino model, two-dimensional Ising model and model of inversion magnetic Earth's field. In computer experiments whose results are presented in this paper, it is used a simplified two-dimensional Ising model, one version of the model related spins. Computer experiments (simulations) are made in the mathematical software Maple. It has been observed reversing the direction of magnetization in a small change of inhomogeneity energy interactions. Consideration of this issue could be of importance for the study of ferromagnetic material.

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Simulation of geomagnetic reversals through magnetic critical models

Cited by 8 publications

References 25 publications

Domino model for geomagnetic field reversals

Domino model for geomagnetic field reversals

Coupled spin models for magnetic variation of planets and stars

Possible Causes of Change in the Direction of Earth's Magnetic Field

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