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

摘要

We study the finite temperature (FT) phase transitions of two-dimensional(2D) $q$-states Potts models on the square lattice, using the first principlesMonte 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 consideredFT phase transitions efficiently. In particular, even with a simple NNconstructed in this investigation, we are able to obtain the relevantinformation of the nature of these FT phase transitions, namely whether theyare first order or second order. Our results strengthens the potentialapplicability of machine learning in studying various states of matters.Subtlety of applying NN techniques to investigate many-body systems is brieflydiscussed as well.