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We present a model to probe metamagnetic properties in systems with anarbitrary number of interacting spins. Thermodynamic properties such as themagnetization per particle $m(B,T,N)$, linear susceptibility $\chi_1(T)$,nonlinear susceptibilities $\chi_3(T)$ and $\chi_5(T)$, specific heat$C(B,T,N)$, and pressure $P(B,T,N)$ were calculated. The model produces adifferent magnetic response for $N$ particles when comparing to $N - 1$particles for small $N \sim 1$. For an even number of particles, thesusceptibilities show maxima in their temperature dependence. An odd numberproduces an additional free spin response that dominates at low temperatures.This free spin response for odd $N$ also produces a step in the magnetizationper particle at $B = 0$. The magnetization shows $N/2$ steps at $\gamma B_c/J =n$ with integer $n$ for even $N$ and $(N-1)/2$ additional steps at half-integer$n$ starting at 3/2 for odd $N$. Small clusters respond with metamagnetism inan otherwise isotropic spin space, while the large clusters show nometamagnetism.

Temperature Dependence of Nonlinear Susceptibilities in an Infinite Range Interaction Model