DOBRUSHIN STATES FOR CLASSICAL SPIN SYSTEMS WITH COMPLEX INTERACTIONS

We consider a classical spin system on the hypercubic lattice with a g eneral interaction of the form [GRAPHICS] where s(x) epsilon{-1, +1} a re the spin variables, beta is the inverse temperature, h is the magne tic field, and lambda(A), are translation-invariant coupling constants satisfying lambda(A) = 0 if diam A > 1. No symmetry relating the conf igurations s = {s(x)} and -s = { -s(x)} is assumed. In dimension d gre ater than or equal to 3, we construct low-temperature states which bre ak the translation invariance of the system by introducing so called D obrushin boundary conditions which force a horizontal interface into t he system. In contrast to previous constructions, our methods work equ ally well for complex interactions, and should therefore be generaliza ble to quantum spin systems.