  The correlation kinetic equation approach is developed that allows describing
spin correlations in a material with hopping transport. The quantum nature of
spin is taken into account. The approach is applied to the problem of the
bipolaron mechanism of organic magnetoresistance (OMAR) in the limit of large
Hubbard energy and small applied electric field. The spin relaxation that is
important to magnetoresistance is considered to be due to hyperfine interaction
with atomic nuclei. It is shown that the lineshape of magnetoresistance depends
on short-range transport properties. Different model systems with identical
hyperfine interaction but different statistics of electron hops lead to
different lineshapes of magnetoresistance including the two empirical laws
$H^2/(H^2 + H_0^2)$ and $H^2/(|H| + H_0)^2$ that are commonly used to fit
experimental results.
