Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder

Details Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder

2011-12-14

arxiv.org/abs/1112.3293v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 5 figures

Scientific paper

With a tight binding treatment we examine amorphous conductors with gas-like disorder, or no correlations among the site positions. We consider an exponentially decaying hopping integral with range $l$, and the Inverse Participation Ratio (IPR) is used to characterize carrier wave functions with respect to localization. With the aid of two complementary finite size scaling techniques to extrapolate to the bulk limit (both methods exploit critical behavior in different ways to find the boundary between domains of extended and localized wave functions) which nevertheless yield identical results, we obtain phase diagrams showing regions where states are extended and domains of localized states. In the 2D case, states are localized below a threshold length scale $l_{c}$ on the order of the interparticle separation $\rho^{-1/2}$ with a finite fraction of states extended for $l > l_{c}$. For $D = 3$, the extended phase is flanked by regions of localized states and bounded by two mobility edges. The swath of extended states, broad for $l \sim 1$, becomes narrower with decreasing $l$, though persisting with finite width even for $l < (1/5)\rho^{-1/3}$. Mobility edges are interpreted as lines of critical points, and we calculate the corresponding critical exponents.

Affiliated with

Also associated with

No associations

Rating

Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-228055