Chern-Simons term in the 4-dimensional SU(2) Higgs model
  Using a variation of Lueschers geometric charge definition for SU(2) lattice gauge theory, we have managed to give a geometric expression for it's Chern-Simons ter. From this definition we have checked the periodic structure. we determined the Chern-Simons density for symmetric and asymmetric lattices near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature. 
F.Karsch, M.L.Laursen, T.Neuhaus, B.Plache and U.-J.Wiese