Machine learning probing universality class of four models

We test details of a possible investigation of the universality using a deep learning approach. We chose an example of the universality class of the two-dimensional 4-state Potts model. There are four known models within the universality class - the 4-state Potts model, the Baxter-Wu model, the Ashkin-Teller model, and the Turban model. We answered part of the questions - accuracy of the critical temperature estimation and correlation length exponent and the possibility of extracting some critical exponents' ratios. We check the accuracy of the approach with learning using the samples generated using one of the models mentioned above and apply the trained network for the testing remaining three models.

L.S. is supported within the framework of State Assignment of Russian Ministry of Science and Higher Education.E.B. and A.D. acknowledge support within the Project Teams framework of MIEM HSE.Simulations were carried out through computational resources of HPC facilities at HSE University.