Chladni states in Ising Spin Lattices

Low-temperature spin dynamics can become trapped in long-lived patterns shaped by the geometry of the interaction network. Here we introduce Chladni states: spin configurations obtained by binarizing the eigenmodes of the interaction Laplacian. These graph-spectral patterns organize the metastable configurations reached by Ising systems under non-ergodic relaxation. The resulting Topological Mode Decomposition provides a compact way to monitor and reconstruct frozen spin configurations in ferromagnets, frustrated antiferromagnets, and spin glasses.