Thermal fluctuations of Chern-Simons numbers in the lattice SU(2) Higgs model

We study the temperature dependence of the Chern-Simons number fluctuations in the SU(2) Higgs model on Euclidean lattices with spatial sizes up to 20³. Temperatures well above the Higgs phase transition T_H are achieved on anisotropic lattices. Numerical results are compared to perturbative results on finite lattices as well as in continuum perturbation theory. We find qualitative agreement with perturbative estimates and see at high temperatures a tendency towards static configurations. Up to temperatures T~=2T_H we find an indication that tunneling between vacuums with different Chern-Simons numbers is still exponentially suppressed.