Phase transitions in transmission lines with long-range fluctuating correlated disorder

In this work we study the localization properties of the disordered classical dual transmission lines, when the values of capacitances {Cj}{Cj} and inductances {Lj}{Lj} fluctuate in phase in the form Cj=C0+bsin(2πxj) and Lj=L0+bsin(2πxj), where b   is the fluctuation amplitude. {xj}{xj} is a disordered long-range correlated sequence obtained using the Fourier filtering method which depends on the correlation exponent αα. To obtain the transition point in the thermodynamic limit, we study the critical behavior of the participation number D  . To do so, we calculate the linear relationship between ln(D)ln(D) versus ln(N)ln(N), the relative fluctuation ηDηD and the Binder cumulant BD. The critical value obtained with these three methods is totally coincident between them. In addition, we calculate the critical behavior of the normalized localization length Λ(b)Λ(b) as a function of the system size N  . With these data we build the phase diagram (b,α)(b,α), which separates the extended states from the localized states. A final result of our work is the disappearance of the conduction bands when we introduce a finite number of impurities in random sites. This process can serve as a mechanism of secure communication, since a little alteration of the original sequence of capacitances and inductances, can destroy the band of extended states.