Distribution of cracks in a chain of atoms at low temperature

We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1\mathrm{/}\beta \in (0,\mathrm{\infty })$. 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 $N\exp (-\beta e_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}\mathrm{/}2)$ with $e_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}>0$ 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.