Session D40 - Poster Session I.
POSTER session, Monday afternoon, March 12
Exhibit Hall, Washington State Convention Center
A tight-binding model H with random nearest-neighbor elements H_ij=\pm 1 is sometimes used in connection with Anderson localization. It is not trivial to say how much disorder this Hamiltonian represents. For example, in 1D, there is no disorder at all, as all elements +1 can be gotten by unitary transformation. We note the connection between characterizing the disorder implied by H on a 2D square lattice and the Ising spin-glass ground-state problem treated by Toulouse. Thus a normal form of H with minimal number of -1 entries is related to the problem of connecting a given set of points on the lattice a minimum total length of string. Several reduction algorithms are discussed. Local densities of states are computed near the ends of strings for the case of low string concentration, hence of low irreducible disorder.