Self-Consistent Screening Calculation of the Critical Exponentη

A self-consistent version of the 1/n expansion is used to calculate the critical exponent η(n,d) for an n-component Ginzburg-Landau field with spatial dimensionality d. The result is exact to first order in 1/n but also includes a partial summation of graphs to all orders in 1/n. This leads to a bounding of η for small n, in contrast to the simple 1/n expansion. Results are η(3,3)0.079, η(2,3)0.11, and η(1,3)0.177. For $d=2$ the theory leads to the conjecture that η vanishes for large values of n.