  We present a numerical study of the $\Delta H(M,\Delta M)$ method and its
ability to accurately determine intrinsic switching field distributions in
interacting granular magnetic materials such as perpendicular recording media.
In particular, we study how this methodology fails for large ferromagnetic
inter-granular interactions, at which point the associated strongly correlated
magnetization reversal cannot be properly represented by the mean-field
approximation, upon which the $\Delta H(M,\Delta M)$ method is based. In this
study, we use a 2-dimensional array of symmetric hysterons that have an
intrinsic switching field distribution of standard deviation $\sigma$ and
ferromagnetic nearest-neighbor interactions $J$. We find the $\Delta H(M,\Delta
M)$ method to be very accurate for small $J/\sigma$ values, while substantial
errors develop once the effective exchange field becomes comparable with
$\sigma$, corroborating earlier results from micromagnetic simulations. We
furthermore demonstrate that this failure is correlated with deviations from
data set redundancy, which is a key property of the mean-field approximation.
Thus, the $\Delta H(M,\Delta M)$ method fails in a well defined and
quantifiable manner that can be easily assessed from the data sets alone.
