Topological transitions in the euclidean 2d U(1)-Higgs model

The two-dimensional U(1)-gauged Higgs model is studied on an euclidean lattice of size $L_1\times L_2$, where the temperature $T=L_2^{-1}$ is of the order of the sphaleron mass. The simulation parameters are taken from zero temperature results. By comparison with classical and semiclassical results I discuss, whether the sphaleron transition rate can be extracted from the behavior of the Chern-Simons number and from the formation of vortices in an euclidean simulation at high temperatures.