Süto András
Research Institute for Solid State Physics and Optics, Budapest, Hungary.
Phys Rev Lett. 2005 Dec 31;95(26):265501. doi: 10.1103/PhysRevLett.95.265501. Epub 2005 Dec 19.
Pair interactions whose Fourier transform is non-negative and vanishes above a wave number K(0) are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three-dimensional example is an interaction of asymptotic form cosK(0)r/r(4). The result is obtained for densities rho > or = rho(d), where rho(1) = K(0)/2(pi), rho(2) = (sq.rt(3)/8)(K(0)/pi)(2), and rho(3) = (1/8sq.rt(2)) x (K(0)/pi)(3). At rho(d) there is a unique periodic GSC which is the uniform chain, the triangular lattice, and the bcc lattice for d = 1,2,3, respectively. For rho > rho(d), the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K(0), and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho > or = (1/6 sq.rt(3)) x (K(0)/pi)(3).
傅里叶变换非负且在波数(K(0))以上消失的对相互作用，在任何维度(d)中都会产生周期性和非周期性的无限体积基态构型（GSC）。一个典型的三维例子是渐近形式为(\cos K(0)r/r^4)的相互作用。该结果是针对密度(\rho\geq\rho(d))得到的，其中(\rho(1)=K(0)/2\pi)，(\rho(2)=(\sqrt{3}/8)(K(0)/\pi)^2)，(\rho(3)=(1/8\sqrt{2})\times(K(0)/\pi)^3)。在(\rho(d))时，分别对于(d = 1,2,3)存在唯一的周期性GSC，即均匀链、三角晶格和体心立方晶格。对于(\rho>\rho(d))，GSC是非唯一的且简并是连续的：任何密度为(\rho)且所有倒易晶格向量不小于(K(0))的周期性构型，以及这种构型的任何并集，都是GSC。面心立方晶格仅对于(\rho\geq(1/6\sqrt{3})\times(K(0)/\pi)^3)是GSC。
