Applications of neural networks to the studies of phase transitions of two-dimensional Potts models

Abstract

We study the finite temperature (FT) phase transitions of two-dimensional (2D) $q$-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We demonstrate that the ideas from NN can be adopted to study these considered FT phase transitions efficiently. In particular, even with a simple NN constructed in this investigation, we are able to obtain the relevant information of the nature of these FT phase transitions, namely whether they are first order or second order. Our results strengthens the potential applicability of machine learning in studying various states of matters. Subtlety of applying NN techniques to investigate many-body systems is briefly discussed as well.

Comments: Revised version, 11 pages, 24 figures