Self-Consistent Screening Calculation of the Critical Exponentη

A self-consistent version of the 1n expansion is used to calculate the critical exponent (n, d) for an n-component Ginzburg-Landau field with spatial dimensionality d. The result is exact to first order in 1n but also includes a partial summation of graphs to all orders in 1n. This leads to a bounding of for small n, in contrast to the simple 1n expansion. Results are (3, 3) 0. 079, (2, 3) 0. 11, and (1, 3) 0. 177. For d=2 the theory leads to the conjecture that vanishes for large values of n.