Efficient Estimation of Classical Spin Hamiltonian based on Bayesian Inference by using Markov Chain Monte Carlo Method*

We propose a method for efficiently estimating a classical spin Hamiltonian based on Bayesian inference using the Markov chain Monte Carlo method. We used sampling data from the exchange Monte Carlo method for the electronic structure calculation in a triangular lattice system. We also used the multidimensional multiple-histogram method which enables the reconstruction of the density of states. Consequently, the results of model selection using all spin configurations could be efficiently reconstructed from sampling data. This suggests that our method can be generically applied to larger systems such as a large-scale numerical simulation system. This method is an extension of our previous methods [1,2].
[1] H. Takenaka, K. Nagata, T. Mizokawa, and M. Okada, J. Phys. Soc. Jpn. 83, 124706, (2014).
[2] H. Takenaka, K. Nagata, T. Mizokawa, and M. Okada, J. Phys. Soc. Jpn. 85, 124003, (2016).