  We study the influence of the choice of transport coefficients (viscosity and
resistivity) on MHD turbulence driven by the magnetorotational instability
(MRI) in accretion disks. We follow the methodology described in paper I: we
adopt an unstratified shearing box model and focus on the case where the net
vertical magnetic flux threading the box vanishes. For the most part we use the
finite difference code ZEUS, including explicit transport coefficients in the
calculations. However, we also compare our results with those obtained using
other algorithms (NIRVANA, the PENCIL code and a spectral code) to demonstrate
both the convergence of our results and their independence of the numerical
scheme. We find that small scale dissipation affects the saturated state of MHD
turbulence. In agreement with recent similar numerical simulations done in the
presence of a net vertical magnetic flux, we find that turbulent activity
(measured by the rate of angular momentum transport) is an increasing function
of the magnetic Prandtl number Pm for all values of the Reynolds number Re that
we investigated. We also found that turbulence disappears when the Prandtl
number falls below a critical value Pm_c that is apparently a decreasing
function of Re. For the limited region of parameter space that can be probed
with current computational resources, we always obtained Pm_c>1. We conclude
that the magnitudes of the transport coefficients are important in determining
the properties of MHD turbulence in numerical simulations in the shearing box
with zero net flux, at least for Reynolds numbers and magnetic Prandtl numbers
that are such that transport is not dominated by numerical effects and thus can
be probed using current computational resources.
