Moore, GD; Hu, C; Müller, B, *Chern-Simons number diffusion with hard thermal loops*,
Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 58 no. 4
(1998),
pp. 450011-4500124 .
**Abstract:**

*We construct an extension of the standard Kogut-Susskind lattice model for classical (3+ 1)-dimensional Yang-Mills theory, in which "classical particle" degrees of freedom are added. We argue that this will correctly reproduce the "hard thermal loop" effects of hard degrees of freedom, while giving a local implementation which is numerically tractable. We prove that the extended system is Hamiltonian and has the same thermodynamics as dimensionally reduced hot Yang-Mills theory put on a lattice. We present a numerical update algorithm and study the Abelian theory to verify that the classical gauge theory self-energy is correctly modified. Then we use the extended system to study the diffusion constant for the Chern-Simons number. We verify the Arnold-Son-Yaffe picture that the diffusion constant is inversely proportional to the hard thermal loop strength. Our numbers correspond to a diffusion constant of Γ = 29±6α5wT4 for m2D= 11g2T2/6.*