Distribution of Cracks in a Chain of Atoms at Low Temperature

Jansen, Sabine; Koenig, Wolfgang; Schmidt, Bernd and Theil, Florian (2021): Distribution of Cracks in a Chain of Atoms at Low Temperature. In: Annales Henri Poincare, Vol. 22, No. 12: pp. 4131-4172

Abstract

We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature 1/beta is an element of (0, infinity). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-beta e(surf)/2) with e(surf) > 0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1424-0637
• Language: English