Classical Sphaleron Rate on Fine Lattices

Details Classical Sphaleron Rate on Fine Lattices Classical Sphaleron Rate on Fine Lattices

1999-06-04

arxiv.org/abs/hep-ph/9906259v1

Phys.Rev. D61 (2000) 105008

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, includes 5 figures

Scientific paper

10.1103/PhysRevD.61.105008

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 beta=32, or lattice spacing a = 1 / (8 g^2 T)) 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 Ambjorn and Krasnitz.

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