Partitioning the phase diagram of pyrochlore and Kitaev magnets using graph theory

Highly frustrated magnets host rich exotic states of matter such as spin liquids and hidden orders. Those phases can occur in various forms and are notoriously difficult to identify. In this talk, I will show that the combination of a kernel method and graph partitioning theory provides an efficient framework to unravel the complex phase diagram of frustrated magnets. It delimits regimes of both classical spin liquids and broken symmetry phases, including hidden orders, and provides the analytical order parameters and/or characteristic local constraints. The method is demonstrated by examples of pyrochlore and Kitaev magnets but applies to general (semi-)classical spin systems.