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Analysis of the phase transition of Potts model with Machine learning

Manda Takashi, Takuya Saito

Published Jan 1, 2020• 0 citations
OpenAlex

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In recent years, developing unsupervised machine learning for identifying phase transition is a research direction. In this paper, we introduce a two-times clustering method that can help select perfect configurations from a set of degenerate samples and assign the configuration with labels in a manner of unsupervised machine learning. These perfect configurations can then be used to train a neural network to classify phases. The derivatives of the predicted classification in the phase diagram, show peaks at the phase transition points. The effectiveness of our method is tested for the Ising, Potts, and Blume-Capel models. By using the ordered configuration from two-times clustering, our method can provide a useful way to obtain phase diagrams.
Machine-learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter.In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, "neural network scaling," which is based on iteratively training convolutional networks of increasing (spatial) complexity and test it on the transverse field Ising chain and q = 6 Potts model.At the continuous Ising transition, our scaling procedure directly reflects the hallmark of a continuous (second-order) phase transition, divergence of a characteristic length scale.Specifically, we extract a classification length scale by measuring the response of the classification accuracy while varying the largest convolution size (architecture of the network).We observe empirically the scaling exponent of the classification length is consistent with a power law with the correlation length exponent ν = 1.Furthermore, we demonstrate the versatility of our algorithm by showing the universal scaling behaviors persist across a variety of measurement bases, including when the order parameter is nonlocal.Finally, we show that the classification length scale remains finite for the q = 6 Potts model, which has a first-order transition and lacks a divergent correlation length.