Sphaleron transition rate at high temperature in the 1+1 D abelian Higgs   model
  New results for the rate are presented using the canonical ensemble in the classical approximation on a spatial lattice. We find that the rate at high temperatures is proportional to $T^2$, and strongly dependent on the lattice spacing $a$. We conclude that a better effective action is needed for the classical approximation. 
Jan Smit and Wai Hung Tang