SIGN PHASE-TRANSITION AND DIRECTED PATHS IN RANDOM-MEDIA

We consider a lattice model which corresponds to the high temperature expansions of disordered Ising and Heisenberg models and to the deeply localized regime of the disordered Anderson model, The spin correlati on functions for the Ising and Heisenberg model and the amplitude of e lectron tunneling for the Anderson model exhibit a ''sign phase transi tion.'' At small concentration x of scatterers with a negative scatter ing amplitude these quantities have predictable signs while at large x their signs are unpredictable. (C) 1996 American Institute of Physics .