Density of states, level-statistics and localization of fractons in 2- and 3-dimensional disordered systems

Extended Fractons and Localized Phonons on Percolation Clusters

“…One intriguing aspect is the vibrational dynamics of percolation networks. Since the pioneering discovery of localized lattice vibrations ("fractons") by Alexander and Orbach [3,4], much work has been devoted to the study of their properties [5][6][7][8][9][10][11][12][13][14] and the investigation of various applications [15][16][17][18]; see [19] for a recent review.It is well accepted that all vibrational excitations are localized at the percolation threshold, and the density of states (DOS) scales as g͑v͒ ϳ v d s 21 , where d s ഠ 4͞3 is the spectral dimension [3][4][5]20]. Above criticality, there exists a crossover frequency v j : for frequencies larger than v j , g͑v͒ ϳ v d s 21 , while below v j the DOS scales in the normal fashion, g͑v͒ ϳ v d21 .…”

“…Analogies with random walks seem to indicate that the crossover characterizes a transition between localized fractons and extended phonons. This view has been mostly accepted for three-dimensional systems [1,2,4,6,13,16,19] (see also [15]), but has not yet been proven. Analogies with the Anderson model [21], in contrast, suggest the absence of a localization-delocalization transition for two-dimensional systems.…”

“…One intriguing aspect is the vibrational dynamics of percolation networks. Since the pioneering discovery of localized lattice vibrations ("fractons") by Alexander and Orbach [3,4], much work has been devoted to the study of their properties [5][6][7][8][9][10][11][12][13][14] and the investigation of various applications [15][16][17][18]; see [19] for a recent review.…”