  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.
