Chern-Simons term in the 4-dimensional SU(2) Higgs Model

Using Seiberg's definition for the geometric charge in SU(2) lattice gauge theory, we have managed to apply it also to the Chern-Simons term. We checked the periodic structure and determined the Chern-Simons density on small lattices $L^4$ and $L^3 \times 2,\, 4$ with $L=4,\, 6,\mbox{ and }8$ near the critical region in the SU(2) Higgs model. The data indicate that tunneling is increased at high temperature.