Coexistence-curve singularities in isotropic ferromagnets

Abstract

The critical behavior of a classical isotropic ferromagnet ($n\ge 2$) is studied to first order in $\epsilon =4-d$. Using renormalization-group recursion relations, we obtain expressions for the equation of state and longitudinal susceptibility which describe singular behavior both at the critical point and on the coexistence curve. It is found that, although the diverging susceptibility on the coexistence curve should not be expected in real magnetic crystals, it can produce a large effect on the initial susceptibility measured below $T_c$ in hexagonal layered crystals such as Cr${\mathrm{Cl}}_3$. Specifically, we find that the susceptibility should diverge as $T\to T_c$ from below as ${\chi }_L\sim {\mathrm{}\left|t\right|\mathrm{}}^{-{\gamma }^{\prime }}$, with ${\gamma }^{\prime }\simeq \gamma +0.79\mathrm{}\simeq 2.12$.