Feynman-Graph Expansion for the Equation of State near the Critical Point

The scaling equation of state for a generalized classical Heisenberg ferromagnet near the critical point is derived by an expansion in $\epsilon =4-d$, where $d$ is the dimension of space. It is shown that, though infrared divergences are induced by the Goldstone modes, the equation of state is divergence free. The results are compared with previous numerical calculations. It is also shown that, for non-Ising-like systems the "linear model" cannot be exact, even at first order in $\epsilon$ (although the numerical deviations from linearity are small).