Correlation asymptotics for non-translation invariant lattice spin   systems
  We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and M{\o}ller this yields asymptotic formulas for the truncated two-point correlation functions of certain non-translation invariant lattice models of real-valued spins. 
Oliver Matte