TABLE II.

Summary of approximate models for the average magnetization parallel to an applied oscillating field $\xi (t)={\xi }_0\hspace{0.17em}\text{cos}\hspace{0.17em}\omega t$.

Abbreviation	$⟨m[\xi (t)]⟩$	Description and validity range
Langevin	$\mathcal{L}[\xi (t)]=\coth \xi (t)-1/\xi (t)$	Equilibrium, frequency is low or field is extremely high
Debye1	$\frac{{\xi }_0}{3}\left(\frac{\hspace{0.17em}\text{cos}\hspace{0.17em}\omega t}{1+{(\omega {\tau }_{\mathrm{B}})}^2}+\frac{\omega {\tau }_{\mathrm{B}}\hspace{0.17em}\text{sin}\hspace{0.17em}\omega t}{1+{(\omega {\tau }_{\mathrm{B}})}^2}\right)$	Linear response, frequency is high or field is extremely low
Debye2	$\mathcal{L}({\xi }_0)\left(\frac{\hspace{0.17em}\text{cos}\hspace{0.17em}\omega t}{1+{(\omega {\tau }_{\mathrm{B}})}^2}+\frac{\omega {\tau }_{\mathrm{B}}\hspace{0.17em}\text{sin}\hspace{0.17em}\omega t}{1+{(\omega {\tau }_{\mathrm{B}})}^2}\right)$	Linear response with Langevin function susceptibility, frequency is high or field is low
EF	$-\int \hspace{0.17em}dt\frac{⟨m(t)⟩}{{\tau }_{\mathrm{B}}}\left(1+\frac{\xi (t)}{{\mathcal{L}}_i(⟨m(t)⟩)}\right)$	Effective field model, quasi equilibrium conditions, requires the inverse Langevin function ${\mathcal{L}}_i$ (see Sec. II C)