Conventionally, the training of a neural network for learning phases of matter uses real physical quantities as the training set. However, it has been demonstrated in several studies that this may not be required. Here we investigate the phase transitions of the two-dimensional (2D) q-state Potts models on the square lattice using a pre-trained neural network (NN). The employed NN was trained previously using two artifically made configurations as the training set. Hence no training is conducted for the present study. Remarkably, the used NN not only calculates the critical points of the considered phase transitions precisely, but also determines the nature of these phase transition definitely without ambiguity. Our results as well as the outcomes found previously suggest that training a NN using real physical quantities as the training set is not required to obtain a working NN. These unconventional studies also imply that if the configuration space of a system can be classified into two categories, then the NN considered here is likely applicable to study the phase transition of that system. Comparison between our approach and other known NN methods for studying the 2D q-state Potts models is briefly discussed as well.
Conventionally, the training of a neural network for learning phases of matter uses real physical quantities as the training set. However, it has been demonstrated in several studies that this may not be required. Here we investigate the phase transitions of the two-dimensional (2D) q-state Potts models on the square lattice using a pre-trained neural network (NN). The employed NN was trained previously using two artifically made configurations as the training set. Hence no training is conducted for the present study. Remarkably, the used NN not only calculates the critical points of the considered phase transitions precisely, but also determines the nature of these phase transition definitely without ambiguity. Our results as well as the outcomes found previously suggest that training a NN using real physical quantities as the training set is not required to obtain a working NN. These unconventional studies also imply that if the configuration space of a system can be classified into two categories, then the NN considered here is likely applicable to study the phase transition of that system. Comparison between our approach and other known NN methods for studying the 2D q-state Potts models is briefly discussed as well.
Abstract The critical phenomena of the 2D antiferromagnetic q-state Potts model on the square lattice with q=2,3,4 are investigated using the techniques of neural networks (NNs). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, whereas the conventional AECs either fail or only work partially to uncover the critical phenomena of the systems associated with q=3 and q=4 investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic q-state Potts models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently.
A neural network study of the phase transitions of the two-dimensional antiferromagnetic q-state Potts models on the square lattice
The critical phenomena of the two-dimensional antiferromagnetic q-state Potts model on the square lattice with q=2,3,4 are investigated using the techniques of neural networks (NN). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, while the conventional AECs fail to uncover the critical phenomena of the systems investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic q-state models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently.
Abstract Using the techniques of neural networks (NN), we study the three-dimensional (3D) five-state ferromagnetic Potts model on the cubic lattice as well as the two-dimensional (2D) three-state antiferromagnetic Potts model on the square lattice. Unlike the conventional approach, here we follow the idea employed by Li et al (2018 Ann. Phys., NY 391 312–331). Specifically, instead of numerically generating numerous objects for the training, the whole or part of the theoretical ground state configurations of the studied models are considered as the training sets. Remarkably, our investigation of these two models provides convincing evidence for the effectiveness of the method of preparing training sets used in this study. In particular, the results of the 3D model obtained here imply that the NN approach is as efficient as the traditional method since the signal of a first order phase transition, namely tunneling between two channels, determined by the NN method is as strong as that calculated with the Monte Carlo technique. Furthermore, the outcomes associated with the considered 2D system indicate even little partial information of the ground states can lead to conclusive results regarding the studied phase transition. The achievements reached in our investigation demonstrate that the performance of NN, using certain amount of the theoretical ground state configurations as the training sets, is impressive.
We study the phase transitions of three-dimensional (3D) classical O(3) model and two-dimensional (2D) classical XY model, as well as both the quantum phase transitions of 2D and 3D dimerized spin-1/2 antiferromagnets, using the technique of supervised neural network (NN). Moreover, unlike the conventional approaches commonly used in the literature, the training sets employed in our investigation are neither the theoretical nor the real configurations of the considered systems. Remarkably, with such an unconventional set up of the training stage in conjunction with some semiexperimental finite-size scaling formulas, the associated critical points determined by the NN method agree well with the established results in the literature. The outcomes obtained here imply that certain unconventional training strategies, like the one used in this study, are not only cost-effective in computation but are also applicable for a wide range of physical systems.
A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.
A Machine Learning study of the two-dimensional antiferromagnetic q-state Potts model on the square lattice
The critical phenomena of two-dimensional (2D) antiferromagnetic q-state Potts model on the square lattice with q=2,3,4,5 and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN approaches, here we train a multilayer perceptron consisting of only one input layer, one hidden layer, and one output layer with two artificially made stagger-like configurations. Remarkably, despite the fact that the MLP is trained without any input from these considered models, it correctly identifies the critical temperatures of the studied physical systems. Particularly, the MLP outcomes suggest convincingly that the q=3 model is critical only at zero temperature and q=4,5,6 models remain disordered at all temperatures. Previously, this MLP has been successfully applied to uncover the nature of the phase transitions of 2D antiferromagnetic Ising model with multi-interactions. Therefore, it will be interesting to examine whether the already trained MLP can detect other models with untypical critical phenomena.