Chern-Simons number diffusion in (1+1)-dimensional Higgs theory

We study the Chern-Simons number diffusion rate in the (1+1)-dimensional latticeAbelian Higgs model at temperatures much higher than, as well as comparable to, the sphaleron energy. It is found that in the high-temperature limit the rate is likely to grow as power 2/3 of the temperature. In the intermediate-temperature regime, our numerical simulations show that very weak temperature dependence of the rate, found in previous work, persists at smaller lattice spacings. We discuss possibilities of relating the observed behavior of the rate to static finite-temperature properties of the model.