EXOTIC STATES IN LONG-RANGE SPIN-GLASSES

We consider Ising spin glasses on Z(d) with couplings J(xy) = c(y-x)Z( xy), where the c(y)'s are nonrandom real coefficients and the Z(xy)'s are independent, identically distributed random variables with E[Z(xy) ] = 0 and E[Z(xy)2] = prove that if SIGMA(y)\c(y)\ = infinity while SI GMA(y)\c(y)\2 < infinity, then (with probability one) there are uncoun tably many (infinite volume) ground states sigma, each of which has th e following property: for any temperature T < infinity, there is a Gib bs state supported entirely on (infinite volume) spin configurations w hich differ from sigma only at finitely many sites. This and related r esults are examples of the bizarre effects that can occur in disordere d systems with coupling-dependent boundary conditions.