Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis

Abstract

This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of unsolved physical models. Toward this goal, we first need to apply the machine learning algorithm to well-understood models and see whether the outputs are consistent with our prior knowledge, which serves as the benchmark of this approach. In this work, we feed the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions. We show that the outputs of the principle component analysis agree very well with our understanding of different orders in different phases, and the temperature dependences of the major components detect the nature and the locations of the phase transitions. Our work offers promise for using machine learning techniques to study sophisticated statistical models, and our results can be further improved by using principle component analysis with kernel tricks and the neural network method.

8 pages, 11 figures

References in corpus (18)

• Machine learning phases of matter
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Multicritical behavior in the fully frustrated XY model and related systems
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-Learning Determinantal Quantum Monte Carlo Method
• Kink pairs unbinding on domain walls and the sequence of phase transitions in fully frustrated XY models
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Recommender Engine for Continuous Time Quantum Monte Carlo Methods
• Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties
• Novel phase transitions in XY Antiferromagnets on Plane Triangulations

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