EXISTENCE OF FREE-ENERGY FOR MODELS WITH LONG-RANGE RANDOM HAMILTONIANS

Classical lattice systems with random Hamiltonians {Mathematical expression} are considered, where d is the dimension, and ε(x1, x2) are independent random variables for different pairs (x1, x2), Eε(x1, x2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, provided α > 1/2. © 1979 Plenum Publishing Corporation.