Electron localisation in systems with purely off-diagonal randomness

A probability distribution for the off-diagonal matrix elements v_nm of the tight binding Hamiltonian is assumed to be $\text{P(v}{}_{\mathrm{nm}}\text{) =}\text{1}\text{Wv}{}_{\mathrm{nm}}$ for $\text{e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}\text{≤ v}{}_{\mathrm{nm}}\text{/v}{}_0\text{≤ e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}$ and P(v_nm = 0 otherwise. A homomorphic cluster CPA with the L(E) criterion is used to study localisation in a simple cubic lattice and a computer simulation is used to study a square lattice with the participation-ratio criterion. It is found, in both cases, that Anderson's transition takes place for a critical degree of disorder.