Detecting phase transitions based on siamese neural network

Abstract Machine learning has been widely applied in physics research. Although unsupervised learning can extract the critical points of phase transitions, the percolation model remains a challenge. Unsupervised learning using the raw configurations of the percolation model fails to capture the critical points. To capture the configuration characteristics of the percolation model, this paper proposes using the maximum cluster as input to the neural network. It is well understood that the order parameter of the percolation model is not simply the particle density, but rather the probability that a given site or bond belongs to the percolating cluster. Additionally, we introduce the use of a Siamese Neural Network (SNN) to detect percolation phase transitions. Unlike unsupervised dimensionality reduction methods or supervised binary classification outputs, the SNN produces a scalar output referred to as similarity. By combining the maximum cluster and the SNN, we not only successfully extract the critical value of the percolation model, but also calculate the correlation exponent via data collapse. We believe that the SNN has great potential in handling phase transition classification problems and can serve as a reference for studying other phase transition systems.