Distribution of cracks in a chain of atoms at low temperature

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.

31 pages

References in corpus (6)

• Crystalline ground states for classical particles
• Face-centered cubic crystallization of atomistic configurations
• $\Gamma$-convergence of the Heitmann-Radin sticky disc energy to the crystalline perimeter
• Emergence of rigid Polycrystals from atomistic Systems with Heitmann-Radin sticky disk energy
• Renewal properties of the $d=1$ Ising model
• Surface energy and boundary layers for a chain of atoms at low temperature