Finite Crystallization via Stratification in Two-Dimensional Square Lattices

Explore a groundbreaking technique for proving two-dimensional crystallization results in the square lattice for finite particle systems. Delve into a 39-minute conference talk from the Workshop on "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Discover how configurational energies with two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice are analyzed. Learn about the innovative stratification method, which associates bond graphs to configurations and modifies them by identifying chains of successive atoms. Understand how this approach reduces the crystallization problem to a simple minimization, corresponding to a proof via slicing of the isoperimetric inequality in l1. Gain insights from the joint work of Manuel Friedrich and Leonard Kreutz in this cutting-edge exploration of finite crystallization.