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Published February 1, 1978 | Published
Journal Article Open

Critical indices from perturbation analysis of the Callan-Symanzik equation


Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained.

Additional Information

© 1978 The American Physical Society. Received 21 June 1977. The authors are happy to acknowledge helpful discussions with D. Bessis, J. des Cloizeaux, P. Moussa, J.L. Lebowitz, D. Parisi, and C. Tracy. We are particularly grateful to E. Brézin, J. C. Le Guillou, and J. Zinn-Justin not only for helpful discussions, but also for making their results available to us before publication. Work supported in part by the U.S. Energy Research and Development Administration, in part by the National Science Foundation, in part by the National Research Council of Canada, and in part by the Commissariat à l'Energie Atomique.

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