Equation of State of a Ferromagnet in the Critical Region

Abstract

It has been suggested that the equation of state of a ferromagnet in the critical region can be put in the form $$\mathrm{\beta mH\hspace{0.17em}=\hspace{0.17em}}{\left(\text{1−t}\right)}^{\Delta }F\left[M^{\text{−1}}{\left(\text{1−t}\right)}^{\mathrm{\Delta -\gamma }}\right]\left({\mathrm{t\hspace{0.17em}=\hspace{0.17em}T}}_c\mathrm{/T}\right)$$ . $\mathrm{F(v)}$ is a function which characterizes the critical behavior, and $\gamma$ and $\Delta$ are two parameters from which all the indices which describe thermodynamic behavior in the critical region can be determined. Griffiths and Helfand have considered possible froms of the function $\mathrm{F(v)}$ . The present investigation makes use of the higher‐order derivatives of magnetization with respect to field as ${\mathrm{T\to T}}_{\mathrm{c+}}$ to provide a series expansion for $\mathrm{F(v)}$ in powers of $\text{v(t<1)}$ ; and of corresponding derivatives as ${\mathrm{T\to T}}_{\mathrm{c-}}$ to provide information about $\mathrm{F(v)}$ near the value corresponding to the spontaneous magnetization $\text{(t>1)}$ . The forms of $\mathrm{F(v)}$ for a number of lattices and models are compared.