CRITICAL EXPONENTS AND THE PSEUDO-ε-EXPANSION

We present the pseudo-epsilon-expansions (tau-series) for the critical exponents of a lambda phi(4)-type three-dimensional O(n)-symmetric model obtained on the basis of six-loop renormalization-group expansions. We present numerical results in the physically interesting cases n = 1, n = 2, n = 3, and n = 0 and also for 4 <= n <= 32 to clarify the general properties of the obtained series. The pseudo-epsilon-expansions or the exponents. and a have coefficients that are small in absolute value and decrease rapidly, and direct summation of the tau-series therefore yields quite acceptable numerical estimates, while applying the Pade approximants allows obtaining high-precision results. In contrast, the coefficients of the pseudo-epsilon-expansion of the scaling correction exponent omega 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 Pade approximants in this case. The pseudo-epsilon-expansion technique can therefore be regarded as a distinctive resummation method converting divergent renormalization-group series into expansions that are computationally convenient.