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

Abstract

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.

arXiv commentThe author had incorrectly neglected the issue of stability concerning which PGSs give rise to extremal Gibbs measures. The error is easily fixed by limiting the scope of Theorem 2.3 to perfect configurations which are stable in the sense of Zahradník. A correction will appear in the near future. We thank Izabella Stuhl and Tyler Helmuth for independently bringing the issue to our attention