Research On Potts Model Phase Transitions Based On Machine Learning

Machine learning is widelyapplied to natural language processing,face recognition,big data processing and many other fields.The machine learning method is one of the most advanced research fields to study the phase transitions problem.In this paper,we mainly apply machine learning methods to study the phase transitions and critical point of the Potts model.The main research contents and results are as follows:1.The Glauber algorithm is applied to study the two-dimensional Potts model.The Monte Carlo simulation results show that the acceptance ratio is quit different in various states of Potts model,and it has great fluctuations near the critical point,where we could estimate critical point of Potts model by the acceptance ratio.Meanwhile,the energy and magnetization have also been investigated using the Glauber algorithm in various temper-ature and states,and we also estimate the critical points of the Potts model.2.The supervised learning has been applied to study the phase transitions of 2-dimens-ional Potts model.The fully connected network and convolutional neural network have been adopted.Results show that the magnetic phase and ferromagnetic phase of Potts model can be identified by the neural network,and the critical point is consistent with that of theory.Furthermore,the neural network can identify the critical point more precisely for small lattice size compared with the Monte Carlo simulation,and as the state q of Potts model increase,the neural network can identify the critical point more precise for the same size.3.The unsupervised learning has been applied to study the phase transitions of 2-dimensional Potts model.The Autoencoder,t-SNE and Principal Component Analysis(PCA)have been adopted.Without any input information,Autoencoder can learn the main features of the spin configuration,and it can identify the low-temperature phase and high-temperature phase.Moreover,different states of Potts model in the low-temperature phase can be distinguished.Homomorphic clustering is observed,and the critical point of Potts model can be estimated by the Autoencoder.PCA and t-SNE can reduce the dimension of Potts configuration and distinguish the low-temperature phase from the high-temperature phase.Homomorphic clustering is also observed.