Critical behavior of the nonlinearσmodel with a free surface: The ‘‘ordinary’’ transition in 2+ε dimensions

We analyze the critical behavior of isotropic ferromagnets with a free surface by means of field-theoretic renormalization methods in d=2+ε dimensions. Renormalization-group equations for surface quantities are derived which imply scaling to all orders in ε. Explicit results to order ${\mathrm{\epsilon }}^2$ are presented for the critical surface exponents of the ordinary transition. Interpolation with the known results near four dimensions yields estimates for d=3 which seem to be remarkably accurate.