论文标题
通过分层有限结晶的证明
A proof of finite crystallization via stratification
论文作者
论文摘要
我们设计了一种新技术来证明有限粒子系统的平方晶格可证明二维结晶。我们将此策略应用于具有两体短粒子相互作用和有利于方形晶格的键角的三体粒子相互作用和三体角电位的配置能量的能量最小化。对于每种配置，我们将其键图关联，然后通过识别连续原子的链条进行适当修改。这种称为分层的方法将结晶问题降低到一个简单的最小化，该最小化与通过切片的等值相对应，以$ \ ell^1 $的切片。作为副产品，我们还证明了对构型能量的最小化（称为$ n^{3/4} $ - 法律）的波动估计。
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice. To each configuration, we associate its bond graph which is then suitably modified by identifying chains of successive atoms. This method, called stratification, reduces the crystallization problem to a simple minimization that corresponds to a proof via slicing of the isoperimetric inequality in $\ell^1$. As a byproduct, we also prove a fluctuation estimate for minimizers of the configurational energy, known as the $n^{3/4}$-law.
