论文标题
低温下原子链中裂纹的分布
Distribution of cracks in a chain of atoms at low temperature
论文作者
论文摘要
我们考虑了一个一维经典的多体系统，其在低温$ 1/β\ in（0，\ infty）$的热力学极限中具有相互作用的潜力。基态是一个周期性的晶格。我们表明，当密度严格小于基态晶格的密度时，带有$ n $颗粒的系统通过将大约结晶域（簇）与空域（空隙）交替，填充空间。域的数量为$ n \ exp（-βe_\ mathrm {surf}/2）$，带有$ e_ \ mathrm {surf}> 0 $ a表面能量。 为了证明，系统将映射到有效模型，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新的邻居相互作用的这些条件，并应用了最近得出的相关性统一估计。
We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1/β\in(0,\infty)$. 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 $N\exp(- βe_\mathrm{surf}/2)$ 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.
