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Distribution of cracks in a chain of atoms at low temperature
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Jansen, Sabine, König, Wolfgang, Schmidt, Bernd and Theil, Florian (2021) Distribution of cracks in a chain of atoms at low temperature. Annales Henri Poincare, 22 . pp. 4131-4172. doi:10.1007/s00023-021-01076-7 ISSN 1424-0637.
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Official URL: https://doi.org/10.1007/s00023-021-01076-7
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/β∈(0,∞). 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 Nexp(−βesurf/2) with esurf>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 | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Atoms -- Effect of low temperatures on, Lattice theory, Crystallography, Mathematical | ||||||||
| Journal or Publication Title: | Annales Henri Poincare | ||||||||
| Publisher: | Springer Basel AG | ||||||||
| ISSN: | 1424-0637 | ||||||||
| Official Date: | December 2021 | ||||||||
| Dates: |
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| Volume: | 22 | ||||||||
| Page Range: | pp. 4131-4172 | ||||||||
| DOI: | 10.1007/s00023-021-01076-7 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 22 July 2021 | ||||||||
| Date of first compliant Open Access: | 22 July 2021 | ||||||||
| Open Access Version: |
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