VACUUM TUNNELING AND PERIODIC STRUCTURE IN LATTICE HIGGS MODELS

Using a geometric definition for the lattice Chern-Simons term in even dimensions, we have studied the distribution of Chern-Simons numbers for the 2d U(1) and the 4d SU(2) lattice Higgs models. The periodic st ructure of the distributions is preserved in our lattice formulation a nd has been examined in detail. In both cases the finite-size effects visible in the distribution of Chern-Simons numbers are well accounted for by the Haar measure. Moreover, we find that [N(CS)2] grows with t he spatial volume. We also find numerical evidence that tunneling in 4 d is increased at high temperature.