Chladni states in Ising Spin Lattices
Statistical Mechanics
2026-05-18 v2 Disordered Systems and Neural Networks
Physics and Society
Abstract
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.
Keywords
Cite
@article{arxiv.2507.05961,
title = {Chladni states in Ising Spin Lattices},
author = {Giulio Iannelli and Pablo Villegas},
journal= {arXiv preprint arXiv:2507.05961},
year = {2026}
}
Comments
6 pages, 4 figures and Supplemental Material