  Persistent homology (PH) is a relatively new field in applied mathematics
that studies the components and shapes of discrete data. In this work, we
demonstrate that PH can be used as a universal framework to identify phases in
spin models, including hidden order such as spin nematic ordering and spin
liquids. By converting a small number of spin configurations to barcodes we
obtain a descriptive picture of configuration space. Using dimensionality
reduction to reduce the barcode space to color space leads to a visualization
of the phase diagram.
