CHERN-SIMONS NUMBER DIFFUSION WITH HARD THERMAL LOOPS - ART. NO. 045001

We construct an extension of the standard Kogut-Susskind lattice model for classical (3 + 1)-dimensional Yang-Mills theory, in which ''class ical 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 t ractable. We prove that the extended system is Hamiltonian and has the same thermodynamics as dimensionally reduced hot Yang-Mills theory pu t on a lattice. We present a numerical update algorithm and study the Abelian theory to verify that the classical gauge theory self-energy i s correctly modified. Then we use the extended system to study the dif fusion 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 Gamma = 29 +/- 6 alpha(w)(5)T(4) for m(D)(2) = 11g(2)T(2) /6. [S0556-2821(98)01814-1].