Renormalization of the NonlinearσModel in2+εDimensions—Application to the Heisenberg Ferromagnets

The nonlinear $\sigma$ model is renormalizable and asymptotically free in two dimensions. We show here how to construct this model in $2+\epsilon$ dimensions. Renormalization-group equations follow and exhibit a nontrivial uv stable fixed point, which corresponds in the language of Heisenberg ferromagnets to a critical point. The existence of systematic expansions in powers of $d-2\mathrm{}$ follows from this analysis. In the presence of a source information about long-distance behavior above the critical coupling constant is obtainable.