Temperature Dependence of Nonlinear Susceptibilities in an Infinite range Interaction model

We present thermodynamic properties of a model with a variable N number of particles, an infinite range antiferromagnetic exchange interaction J and under the influence of an external magnetic field B . We have calculated the magnetization m (B,T,N), more specifically, the temperature dependent linear susceptibility χ ₁(T) and nonlinear susceptibilities₎ χ₃ (T) and χ₅ (T). For an even number of particles the susceptibilities show maxima in their temperature dependence. For an odd number of particles there is an additional free spin response that dominates at low temperatures. In magnetization, for odd number of particles, there is a step at B = 0, followed by steps at critical fields B_c = 3J/2γ, 5J/2γ… (2n+1)J/2γ. Thus small clusters respond with metamagnetism in an otherwise isotropic spin space, while the largest clusters show no metamagnetism.