Critical exponents and the pseudo-ǫ expansion

We present the pseudo-ǫ expansions (τ -series) for the critical exponents of a λφ4 threedimensional O(n)-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases n = 1, n = 2, n = 3 and n = 0, as well as for 4 ≤ n ≤ 32 in order to clarify the general properties of the obtained series. The pseudo-ǫ-expansions for the exponents γ α have small and rapidly decreasing coefficients. So, even the direct summation of the τ -series leads to fair estimates for critical exponents, while addressing Pade approximants enables one to get high-precision numerical results. In contrast, the coefficients of the pseudo-ǫ expansion of the scaling correction exponent ω do not exhibit any tendency to decrease at physical values of n. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Padé approximants in this case. The pseudo-ǫ expansion technique can therefore be regarded as a specific resummation method converting divergent renormalization-group series into expansions that are computationally convenient. ∗Electronic address: [email protected]