Localization-delocalization transition in a two-dimensional quantum percolation model

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 6, 2008, Pages

  Islam, M Fhokrul ^a   Nakanishi, Hisao ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HOPPING TRANSPORT; LOCALIZATION-DELOCALIZATION TRANSITIONS; PERCOLATION CLUSTERS; QUANTUM PERCOLATION; TRANSMISSION COEFFICIENTS; TRIANGULAR LATTICES; TWO DIMENSIONS; TWO-DIMENSIONAL (2D);

EID: 44949180685     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.061109     Document Type: Article

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30. For exponential and power laws, the motivation comes from a picture where the transmission arises from overlapping wave functions. Then the overlap integral will decay exponentially with the distance if the wave functions are themselves exponential. It will decay by a power law if they are power-law or long-ranged. The motivation for fitting to an exponential plus a constant offset to test for delocalization can be understood by a simple analogy to, say, the correlation function of an Ising model below Tc. If there were finite order (transmission, here), then there would be a constant offset. Except for this "order", the correlation should behave very similarly to the "disordered" phase since the critical correlation of the fluctuations should only occur at Tc and not for T< Tc or T> Tc. That is, if we subtract the offset, the remainder should decay the same way as it does above Tc, i.e., exponentially. Of course, in our problem, this analogy may not be true and some sort of residual long-range correlations may still exist after subtracting the offset, which might require a power-law plus offset instead. However, our first guess would be to use an exponential plus offset.