Scaling behavior of the localization length in random dimer harmonic chains with thermal correlations

The nature of the vibrational modes of a random dimer harmonic chain with thermal correlations is numerically investigated. It is obtained that the localization length L(c) does not scale with the annealing temperature T like the mean cluster size xi(a) (In xi proportional to 1/T). Instead, it obeys distinct scaling laws, namely L(c)(omega,T)proportional to T(-vc)L(c)(omega,infinity), with v(c)= 2.7 and v(c) = 3.9 both in the bottom and upper halves common band, respectively.