Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions

We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant gB for which we possess a finite number L of expansion coefficients plus two more information: the knowledge of the large-order behavior proportional to (−α)kk!kβgBk, with a known growth parameter α, and the knowledge of the approach to scaling of the type c+c′/gBω, with constants c,c′ and a critical exponent of approach ω. The latter information leads to an increase in the speed of convergence and a high accuracy of the results. The algorithm is applied to the six- and seven-loop expansions for the critical exponents of O(N)-symmetric φ4-theories, and the result for the critical exponent α is compared with a recent satellite experiment.