Detecting hidden and composite orders in layered models via machine learning. (arXiv:1907.05417v1 [cond-mat.dis-nn])

We use machine learning to study layered spin models where composite order
parameters may emerge as a consequence of the interlayerer coupling. We focus
on the layered Ising and Ashkin-Teller models, determining their phase diagram
via the application of a machine learning algorithm to the Monte Carlo data.
Remarkably our technique is able to correctly characterize all the system
phases also in the case of hidden order parameters, \emph{i.e.}~order
parameters whose expression in terms of the microscopic configurations would
require additional preprocessing of the data fed to the algorithm. Within the
approach we introduce, owing to the construction of convolutional neural
networks, naturally suitable for layered image-like data with arbitrary number
of layers, no preprocessing of the Monte Carlo data is needed, also with regard
to its spatial structure. The physical meaning of our results is discussed and
compared with analytical data, where available. Yet, the method can be used
without any \emph{a priori} knowledge of the phases one seeks to find.

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