Ground state structure of random magnets

Using exact optimization methods, we find all of the ground states of (+/- h) random-field Ising magnets (RFIM) and of dilute antiferromagnets in a field (DAFF). The degenerate ground states:are usually composed of isolated clusters (two-level systems) embedded in a frozen background. We calculate the paramagnetic response (sublattice response) and the ground state entropy for the RFIM (DAFF) due to these clusters. In both two and three dimensions there is a broad regime in which these quantities are strictly positive, even at irrational values of h/J (J is the exchange constant). [S1063-651X(98)05610-4].