Temperature dependence of nonlinear susceptibilities in an infinite range interaction model

We present a model to probe metamagnetic properties in systems with a variable number of interacting spins. Thermodynamic properties such as the magnetization per particle [Formula: see text], linear susceptibility [Formula: see text], and nonlinear susceptibilities [Formula: see text] and [Formula: see text] were calculated. The model produces a different magnetic response for N particles when comparing to N  -  1 particles for small [Formula: see text]. For an even number of particles, the susceptibilities show maxima in their temperature dependence. An odd number produces an additional free spin response that dominates at low temperatures. This free spin response also produces a step in the field-dependent magnetization per particle at B  =  0 for odd N. The magnetization shows N/2 steps at [Formula: see text] with integer n for even N and [Formula: see text] additional steps at [Formula: see text] with integer n for odd N. Small clusters respond with metamagnetism in an otherwise isotropic spin space, while the large clusters show no metamagnetism.