Infrared bounds and the peierls argument in two dimensions

We propose a definition of contours for spin systems which leads to improved estimates on the region of parameters where several phases coexist. We discuss as examples anisotropic rotators and a ⁴ lattice field theory. Our contours are estimated using infrared bounds and they are related to those of Euclidean Field Theory.Part of this work was done while Jean Bricmont was at the Mathematics Department of Princeton University and Jean-Raymond Fontaine was at the Mathematics Department of Rutgers University. This work was supported by NSF Grant No. MCS 78-01885 at Princeton University and by NSF Grant No. PHY 78-15920 at Rutgers University