Department of Physics, University of Warwick, Coventry, CV4 7AL, UK.
J Phys Condens Matter. 2012 Oct 10;24(40):405401. doi: 10.1088/0953-8984/24/40/405401. Epub 2012 Sep 18.
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of ν = 1.550(-0.017)(+0.020) confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.
我们通过数值方法研究了在具有调和耦合的三维立方晶格中，质量和弹簧常数无序引起的局域-离域相变。结果表明，尽管相图显示了稳定和不稳定波的区域，但在所有相边界处，质量和弹簧常数无序的转变具有相同的普遍性。局域长度临界指数的组合值 ν = 1.550(-0.017)(+0.020) 证实了与标准电子安德森局域化模型的普遍性类的一致性。我们还通过研究态密度、参与数和波函数统计进一步支持了我们的研究。
