  (abridged) The ICM has been suggested to be buoyantly unstable in the
presence of magnetic field and anisotropic thermal conduction. We perform first
cosmological simulations of galaxy cluster formation that simultaneously
include magnetic fields, radiative cooling and anisotropic thermal conduction.
In isolated and idealized cluster models, the magnetothermal instability (MTI)
tends to reorient the magnetic fields radially. Using cosmological simulations
of the Santa Barbara cluster we detect radial bias in the velocity and magnetic
fields. Such radial bias is consistent with either the inhomogeneous radial gas
flows due to substructures or residual MTI-driven field rearangements that are
expected even in the presence of turbulence. Although disentangling the two
scenarios is challenging, we do not detect excess bias in the runs that include
anisotropic thermal conduction. The anisotropy effect is potentially detectable
via radio polarization measurements with LOFAR and SKA and future X-ray
spectroscopic studies with the IXO. We demonstrate that radiative cooling
boosts the amplification of the magnetic field by about two orders of magnitude
beyond what is expected in the non-radiative cases. At z=0 the field is
amplified by a factor of about 10^6 compared to the uniform magnetic field
evolved due to the universal expansion alone. Interestingly, the runs that
include both radiative cooling and anisotropic thermal conduction exhibit
stronger magnetic field amplification than purely radiative runs at the
off-center locations. In these runs, shallow temperature gradients away from
the cluster center make the ICM neutrally buoyant. The ICM is more easily mixed
in these regions and the winding up of the frozen-in magnetic field is more
efficient resulting in stronger magnetic field amplification.
