2017/01/25 by Ryo Tamura, Koji Hukushima
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Ising model #Machine Learning in Materials Science #Magnetization #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Physics #Quantum mechanics #Spin (aerodynamics) #Statistical physics #Statistics #Surface and Thin Film Phenomena #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.95.064407
published as Physical Review B 95, 064407 (2017) · 9 pages, 7 figures
arxiv created 2017/01/25 · openalex publication_date 2017/02/08 · arxiv updated 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 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 l1 regularization in the prior distribution.