Feynman-Graph Expansion for Critical Exponents

The critical exponents $\gamma$, $\eta$ and the "crossover index" $\varphi$ are computed for generalized classical Heisenberg models with $n$ internal degrees of freedom as an exact expansion in $\epsilon =4-d$ ($d$ is the number of space dimensions). Results are obtained to order ${\epsilon }^2$ for $\gamma$ and to order ${\epsilon }^3$ for $\eta$. The results to this order for the three-dimensional Ising case ($n=\epsilon =1\mathrm{}$) are $\gamma =1.244\mathrm{}$ and $\eta =0.037\mathrm{}$.

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