A system of N non-interacting classical spins, where each spin can take values σ = −1, 0, 1, is placed in a magnetic field h. The single spin Hamiltonian is given by
\(H=-\mu_B h σ+\Delta\left(1-σ^2\right)\),
where μB. Δ are positive constants with appropriate dimensions. If M is the magnetization, the zero-field magnetic susceptibility per spin \(\begin{equation} \left.\frac{1}{N} \frac{\partial M}{\partial h}\right|_{h \rightarrow 0} \end{equation}\), at a temperature T = 1/βkB is given by
1
\(\beta \mu_B^2\)
2
\(\frac{2 \beta \mu_B^2}{2+e^{-\beta \Delta}}\)
3
\(\beta \mu_B^2 e^{-\beta \Delta}\)
4
\(\frac{\beta \mu_B^2}{1+e^{-\beta \Delta}}\)