Method for estimating spin-spin interactions from magnetization curves

@article{Tamura2017MethodFE,
  title={Method for estimating spin-spin interactions from magnetization curves},
  author={Ryo Tamura and Koji Hukushima},
  journal={Physical Review B},
  year={2017},
  volume={95}
}
We develop a method to estimate the spin-spin interactions in the Hamiltonian from the observed magnetization curve by machine learning based on Bayesian inference. In our method, plausible spin-spin interactions are determined by maximizing the posterior distribution, which is the conditional probability of the spin-spin interactions in the Hamiltonian for a given magnetization curve with observation noise. The conditional probability is obtained by the Markov-chain Monte Carlo simulations… 

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References

SHOWING 1-10 OF 41 REFERENCES

Model Selection of NiGa2S4 Triangular Lattice by Bayesian Inference

We propose a novel method for extracting effective classical spin Hamiltonians from mean-field type electronic structural calculations by means of the Bayesian inference. We apply the method for a

Designer spin systems via inverse statistical mechanics

In this work, we extend recent inverse statistical-mechanical methods developed for many-particle systems to the case of spin systems. For simplicity, we focus in this initial study on the two-state

Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification

In the first paper of this series (DiStasio, Jr., Marcotte, Car, Stillinger, and Torquato, Phys. Rev. B 88, 134104 (2013)), we applied inverse statistical-mechanical techniques to study the extent to

Magnetization Process in an Ising Spin System

total number of negative spins and the numbers of interaction lines connecting either two negative spins or negative and positive spins. It is shown by use of topological relations among these

Magnetic Properties of the Spin-1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Trimerized Heisenberg Chain

  • K. Hida
  • Physics, Materials Science
  • 1994
The magnetic properties of the ferromagnetic-ferromagnetic-antiferromagnetic trimerized spin-1/2 Heisenberg chain are studied theoretically. The high temperature susceptibilty and the ground state

Random fan-out state induced by site-random interlayer couplings

We study the low-temperature properties of a classical Heisenberg model with site-random interlayer couplings on the cubic lattice. This model is introduced as a simplified effective model of

Physics-based statistical learning approach to mesoscopic model selection.

It is shown that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model.

Machine-learning approach for one- and two-body corrections to density functional theory: Applications to molecular and condensed water

We show how machine learning techniques based on Bayesian inference can be used to enhance the computer simulation of molecular materials, focusing here on water. We train our machine-learning

Bayesian inference in processing experimental data: principles and basic applications

The aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as the following: model comparison, including the automatic Ockham's Razor filter provided by the Bayesian approach.

Bayesian inference in physics: case studies

Parameter estimation within the Bayesian framework is shown to allow for the incorporation of expert knowledge which in turn allows the treatment of under-determined problems which are inaccessible by the traditional maximum likelihood method.