1. Distribution of cracks in a chain of atoms at low temperature
- Author
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Jansen, Sabine, König, Wolfgang, Schmidt, Bernd, and Theil, Florian
- Subjects
Mathematical Physics ,Mathematics - Analysis of PDEs ,Mathematics - Probability ,82B21, 74B20, 74G65, 60F10 - Abstract
We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1/\beta\in(0,\infty)$. 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 $N\exp(- \beta e_\mathrm{surf}/2)$ with $e_\mathrm{surf}>0$ 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., Comment: 31 pages
- Published
- 2020
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