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arXiv · hep-ph/9906259

Classical Sphaleron Rate on Fine Lattices

Guy D. Moore·Kari Rummukainen
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Abstract

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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Guy D. Moore, Kari Rummukainen. 1999-06-04. Classical Sphaleron Rate on Fine Lattices. https://doi.org/10.1103/physrevd.61.105008

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