Application of the variational autoencoder to detect the critical points of the anisotropic Ising model

Anshumitra Baul; Nicholas Walker; Juana Moreno; Ka-Ming Tam

doi:10.1103/PhysRevE.107.045301

Application of the variational autoencoder to detect the critical points of the anisotropic Ising model

Phys Rev E. 2023 Apr;107(4-2):045301. doi: 10.1103/PhysRevE.107.045301.

Authors

Anshumitra Baul¹, Nicholas Walker², Juana Moreno³, Ka-Ming Tam³

Affiliations

¹ Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
² Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
³ Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA, and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA.

PMID: 37198781
DOI: 10.1103/PhysRevE.107.045301

Abstract

We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of (d+1)-dimensional anisotropic models can be mapped to that of the d-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via the quantum Monte Carlo method.