Abstract
The occurrence probability P-n of necklace states (NS) and the logarithm-conductance distribution P-ln G in one-dimensional random configurations are investigated. Theoretically and numerically, we find that both P-n and P-ln G do not follow 'single parameter scaling' theory generally, since they depend on localization length xi even with the same L/xi, where L is system length. Based on theoretical P-n, our prediction of the behavior of typical conductance, dominated by NS, agrees very well with numerical results. Our theoretical and numerical results support the critical role of NS in Anderson phase transition.