Exploring percolation phase transition in the three-dimensional Ising model with machine learning

The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase transition in the 3D cubic Ising model by employing two machine learning techniques. Our results demonstrate the capability of machine learning methods in distinguishing different phases during the percolation transition. Through the finite-size scaling analysis on the output of the neural networks, the percolation temperature and a correlation length exponent in the geometrical percolation transition are extracted and compared to those in the thermal magnetization phase transition within the 3D Ising model. These findings provide a valuable way essential for enhancing our understanding of the property of the QCD critical point, which belongs to the same universality class as the 3D Ising model.