Critical Exponents of the N-vector model

TL;DR

This paper refines the critical exponents of the N-vector model using extended seven-loop series and improved Borel summation, showing better agreement with epsilon-expansion results and reduced errors in key exponents.

Contribution

It introduces new summation techniques and updates critical exponent estimates with higher-order series, improving accuracy and consistency with epsilon-expansion.

Findings

Exponents like eta have reduced errors and improved estimates.

Summation errors are better quantified, enhancing reliability.

Agreement between 3D series and epsilon-expansion has improved.

Abstract

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.