Machine Learned Phase Transitions in a System of Anisotropic Particles on a Square Lattice

Abstract

The area of Machine learning (ML) has seen exceptional growth in recent years. Successful implementation of ML methods in various branches of physics has led to new insights. These methods have been shown to classify phases in condensed matter systems. Here we study the classification problem of phases in a system of hard rigid rods on a square lattice around a continuous and a discontinuous phase transition using supervised learning (with prior knowledge about the transition points). On comparing a number of ML models we find that convolutional neural network (CNN) classifies the phases with the highest accuracy when only snapshots are given as inputs. We study how the system size affects the model performance. We compare the performance of CNN in classifying the phases around a continuous and a discontinuous phase transition. Further, we show that one can even beat the accuracy of CNN with simpler models by using physics-guided features. Lastly, we show that the critical point in this system can be learned without any prior estimate by using only the information of the ordered phase (as training set). Our study reveals the ML techniques that have been successful in studying spin systems can be easily adapted to more complex systems.

The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice

“…The transition has been rigorously established to exist in two dimensions [11], and is also seen in the exactly soluble case of k-mers on tree-like lattices [12]. It has also been shown that machine learning can be used to detect this phase transition [13].…”

Generalization capabilities of translationally equivariant neural networks

“…Often times the data are flattened somewhere in the network, as e.g. in [21][22][23][24][25][26], and sometimes a convolutional or pooling operation with a stride greater than one spoils symmetry under translations, even though a global pooling layer constitutes the transition from the convolutional part of the network to its dense part, e.g. in [27].…”