Machine learning the Mattis glass transformation

Machine learning techniques are being actively explored to ascertain their usefulness in many areas of physics. Within condensed matter physics, one of the goals these techniques are being investigated for is per their ability to identify the different phases of a system. As such, the identification of a system's symmetries and underlying gauges is taken as a crucial step to accomplish this endeavor. In this context, we consider classical spin models in which we introduce a so-called Mattis gauge transformation. This transformation turns the standard ferromagnetic Ising model into a non-frustrated random bond Ising model, and the ferromagnetic XY model into an XY model with random Dzyaloshinskii-Moriya interactions. We show through a simple unsupervised method, the Principal Component Analysis (PCA), that PCA is able to expose the introduced, albeit hidden, gauge transformation for both models. For the Ising Mattis-model, the original Ising model structure is recovered by PCA, and a rough estimate of the gauge distribution is extracted. For the XY gauge model, we show that while the gauge transformation is ``hidden’’ in the clustering structure for the full data set, it is nevertheless uncovered when studying a specific component of the spins.