Method for estimating spin-spin interactions from magnetization curves

We develop a method to estimate the spin-spin interactions in the Hamiltonian from the observedmagnetization 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 givenmagnetization curve with observation noise. The conditional probability is obtained with 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 showthat 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.