Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures

We present a unified extension of two sets of criteria for high-fugacity crystallization in hard-core lattice systems developed previously by Jauslin, Lebowitz, and the author. Our new criterion is formulated in terms of the existence of a volume allocation rule with desirable optimization and screening properties, in analogy to the scoring function constructed in Hales’ proof of the Kepler conjecture. Notably, our result applies to a large class of polyomino models with discrete rotational degrees of freedom and their chiral mixtures, as well as multi-component mixtures featuring several geometrically distinct particle shapes. The proof uses a recent systematic extension of Pirogov–Sinai theory to systems with infinite interactions by Mazel–Stuhl–Suhov.