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arXiv · 2011.12213

Distribution of cracks in a chain of atoms at low temperature

Sabine Jansen·Wolfgang König·Bernd Schmidt·Florian Theil
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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.

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Sabine Jansen, Wolfgang König, Bernd Schmidt, Florian Theil. 2020-11-24. Distribution of cracks in a chain of atoms at low temperature. https://doi.org/10.1007/s00023-021-01076-7

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