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 g(B) for which we possess a finite number L of expansion coefficients plus two more information: the knowledge of the large-order behavior proportional to (-alpha)(k)k!k(beta)g(B)(k), with a known growth parameter alpha, and the knowledge of the approach to scaling of the type c + c'/g(B)(omega), with constants c,c(') and a critical exponent of approach omega. 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 phi (4)-theories, and the result for the critical exponent alpha is compared with a recent satellite experiment. (C) 2001 American Institute of Physics.