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

## TL;DR

This paper demonstrates that principal component analysis can effectively identify phase transitions and order parameters in frustrated classical spin models, serving as a benchmark for AI-based phase recognition without prior knowledge.

## Contribution

It shows that PCA applied to Monte Carlo data accurately detects phase transitions in frustrated XY models, validating machine learning for complex statistical physics systems.

## Key findings

- PCA outputs align with known phase structures.
- Temperature dependence of principal components reveals phase transition points.
- Method provides a benchmark for AI recognition of phases in complex models.

## 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.