One-dimensional DLR invariant measures are regular

A system of infinite spins in one dimension is considered. The interaction is given by a pair potential –J _xyS_xS_y, whereS _x,S _y are the spins at the sitesx,y andJ _xy=J(|x–y|) whereJ(|x–y|) decreases asymptotically in an integrable way. The self-interaction makes the system superstable. It is proven that any invariant DLR measure for this system satisfies Ruelle's superstable estimates (regularity condition).