Classical Sphaleron Rate on Fine Lattices

We measure the sphaleron rate for hot, classical Yang-Mills theory on the lattice, in order to study its dependence on lattice spacing. By using a topological definition of Chern-Simons number and going to extremely fine lattices (up to β = 32, or lattice spacing a = 1/(8gT )) we demonstrate nontrivial scaling. The topological susceptibility, converted to physical units, falls with lattice spacing on fine lattices in a way which is consistent with linear dependence on a (the Arnold-Son-Yaffe scaling relation) and strongly disfavors a nonzero continuum limit. We also explain some unusual behavior of the rate in small volumes, reported by Ambjørn and Krasnitz. MCGILL-99/21 NORDITA-99/33HE June 1999 MCGILL-99/21 NORDITA-99/33HE hep-ph/9906259 email: [email protected] email: [email protected]