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.

我们考虑在低温\(1/\beta \in (0,\infty )\)的热力学极限中具有Lennard-Jones 型相互作用势的一维经典多体系统。基态是周期性晶格。我们表明，当密度严格小于基态晶格的密度时，具有N粒子的系统通过将近似结晶域（簇）与由于断裂键造成的空域（空隙）交替来填充空间。域的数量为\(N\exp (- \beta e_\mathrm {surf}/2)\)与\(e_\mathrm {surf}>0\)表面能。为了证明，该系统被映射到一个有效模型，该模型是缺陷的低密度晶格气体。结果需要关于缺陷之间相互作用的条件。我们成功地验证了下一个最近邻相互作用的这些条件，应用了最近得出的相关性的统一估计。