A comparison of bond and site CPAS for dilute systems

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Abstract
The properties of the bond CPA (BCPA) have been investigated in the Goldstone case and for pure off-diagonal disorder. The results have been compared with those obtained using other methods. The moments of the density of states obtained using different CPA theories have been compared with the exact ones. The numerical comparison of the BCPA and Lage-Stinchcombe (LS) theory in the case of pure off-diagonal disorder shows that unlike LS theory the BCPA gives a gap and the delta -like peak at E=0 for the concentration below the approximate percolation concentration which is in rough agreement with computer simulations. The properties of the gap and peak have been obtained analytically. The BCPA appears to be a useful working approximation for the Goldstone and off-diagonal disorder problem but not for the site diagonal case usually treated in the SCPA.