# Method for Estimating Spin-Spin Interactions from Magnetization Curves

## TL;DR

This paper introduces a machine learning approach using Bayesian inference and Monte Carlo methods to accurately estimate spin-spin interactions in magnetic systems from noisy magnetization data.

## Contribution

It presents a novel method combining Bayesian inference, MCMC, and $l_1$ regularization to determine relevant spin interactions from magnetization curves.

## Key findings

- High accuracy in estimating spin-spin interactions.
- Effective selection of relevant interaction terms.
- Validated with synthetic data.

## Abstract

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 combined with an exchange Monte Carlo method. The efficiency of our method is tested using synthetic magnetization curve data, and the results show that spin-spin interactions are estimated with a high accuracy. In particular, the relevant terms of the spin-spin interactions are successfully selected from the redundant interaction candidates by the $l_1$ regularization in the prior distribution.