Detecting hidden and composite orders in layered models via machine learning

W. Rzadkowski, N. Defenu, S. Chiacchiera, A. Trombettoni, G. Bighin

Published 2019-07-11Version 1

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.