Fast-Convergent Resummation Algorithm and Critical Exponents of φ-Theory in Three Dimensions

Abstract 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 informations: The knowledge of the large-order behavior proportional to (−α)kk!kβgk B, with a known growth parameter α, and the knowledge of the approach to scaling being of the type c + c/g B, 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 sixand seven-loop expansions for the critical exponents of O(N)-symmetric φ-theories, and the result for the critical exponent α is compared with the recent satellite experiment.