On the absence of non-translational invariant Gibbs states in two dimensions

We consider an Ising system in $\nu=2$ dimensions with a ferromagnetic Kac potential whose scaling parameter is denoted by $\gamma$. We will show that for any $\ga$ sufficiently small every Gibbs state is translational invariant. Taking account of the result on the phase diagram \cite{BMP}, our result implies that below the critical temperature, for any $\ga$ sufficiently small there exist only two pure phases