  We report two fundamental inequalities in the Stoner-Wohlfarth model.
Specifically, we investigate the theoretical limit for the initial magnetic
susceptibility in a system described by the Stoner-Wohlfarth approach. We also
find analytical solutions for the magnetization in the low-field regime and
obtain the borderline value for the uniaxial anisotropy constant in such an
ideal Stoner-Wohlfarth system. We go beyond and introduce a general mean-field
theory for interacting Stoner-Wohlfarth-like systems, thus estimating how the
initial magnetic susceptibility is affected by the dipolar and exchange
interactions inside the system. By means of a simple insight from a fundamental
inequality for the magnetic susceptibility of an ideal Stoner-Wohlfarth system,
we show its violation is a signature of the existence of exchange interactions
between nanoparticles in an interacting Stoner-Wohlfarth-like system.
