Fisher exponent from pseudo-ε expansion

The critical exponent η for three-dimensional systems with an n-vector order parameter is evaluated in the framework of the pseudo-ε expansion approach. The pseudo-ε expansion (τ series) for η found up to the τ(7) term for n = 0, 1, 2, 3 and within the τ(6) order for general n is shown to have a structure that is rather favorable for getting numerical estimates. The use of Padé approximants and direct summation of the τ series result in iteration procedures rapidly converging to the asymptotic values that are very close to the most reliable numerical estimates of η known today. The origin of such an efficiency is discussed and shown to lie in the general properties of the pseudo-ε expansion machinery interfering with some peculiarities of the renormalization group expansion of η.