  The spin structures of small spin-1 condensates ($N\leq 1000$) under a
magnetic field $B$ has been studied beyond the mean field theory (MFT). Instead
of the spinors, the many body spin-eigenstates have been obtained. We have
defined and calculated the spin correlative probabilities to extract
information from these eigenstates. The correlation coefficients and the
fidelity susceptibility have also been calculated. Thereby the details of the
spin-structures responding to the variation of $B$ can be better understood. In
particular, from the correlation coefficients which is the ratio of the 2-body
probability to the product of two 1-body probabilities, strong correlation
domains (SCD) of $B$ are found. The emphasis is placed on the sensitivity of
the condensates against $B$. No phase transitions in spin-structures are found.
However, abrupt changes in the derivatives of observables (correlative
probabilities) are found in some particular domains of $B$. In these domains
the condensates are highly sensitive to $B$. The effect of temperature is
considered. The probabilities defined in the paper can work as a bridge to
relate theories and experiments. Therefore, they can be used to discriminate
various spin-structures and refine the interactions.
