Critical Behavior of a Classical Heisenberg Ferromagnet with Many Degrees of Freedom

The critical behavior of a classical Heisenberg ferromagnet is studied in the limit where the spin dimensionality $N$ is large. Corrections of order $\frac{1}{N}$ to the spherical model are obtained as functions of a continuous dimension $d$, $2<d<\mathrm{}4\mathrm{}$. Particular attention is given to the behavior near the coexistence curve. The divergence of the magnetic susceptibility below $T_c$ as the external field vanishes is discussed through a nonlinear realization of the $O\left(N\right)\mathrm{}$ symmetry, as well as in the $\frac{1}{N}$ and $4-d$ expansions.