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Media type:
E-Article
Title:
Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions
Contributor:
Jasch, Florian;
Kleinert, Hagen
imprint:
AIP Publishing, 2001
Published in:Journal of Mathematical Physics
Language:
English
DOI:
10.1063/1.1289377
ISSN:
0022-2488;
1089-7658
Origination:
Footnote:
Description:
<jats:p>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.</jats:p>