The Anderson transition in a model of coupled random polymer chains

We obtain by transfer matrix scaling methods the Anderson metal-insulator phase diagram for a random electronic tight binding Hamiltonian, modelling a 'spaghetti' of random polymer chains having randomly placed cross-links J with concentration c. If J is small and c is large the results depend on the product J . c as predicted by a mean-field approach. For large J and small c this dependence breaks down as a result of the large off-diagonal disorder introduced by the random cross-linkings. The localization length critical exponent in this highly anisotropic model takes the universal three-dimensional value v = 1.3 +/- 0.2.