Fast-Convergent Resummation Algorithm and Critical Exponents of phi^4-Theory in Three Dimensions

TL;DR

This paper introduces a fast algorithm for resumming divergent series in phi^4-theory, improving convergence and accuracy in calculating critical exponents, and compares results with experimental data.

Contribution

The paper presents a novel resummation algorithm that incorporates large-order behavior and scaling approach information to enhance convergence in phi^4-theory calculations.

Findings

Achieved high-precision critical exponents for O(N) models.

Validated the algorithm by comparing with recent experimental results.

Demonstrated improved convergence speed over traditional methods.

Abstract

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 informations: The knowledge of the large-order behavior proportional to (- alpha)^kk!k^beta g_B^k, with a known growth parameter alpha, and the knowledge of the approach to scaling being 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 the recent satellite experiment.