  It was proved \cite{EMYa, QY} that stochastic lattice gas dynamics converge
to the Navier-Stokes equations in dimension $d=3$ in the incompressible limits.
In particular, the viscosity is finite. We proved that, on the other hand, the
viscosity for a two dimensional lattice gas model diverges faster than $\log
\log t$. Our argument indicates that the correct divergence rate is $(\log
t)^{1/2}$. This problem is closely related to the logarithmic correction of the
time decay rate for the velocity auto-correlation function of a tagged
particle.
