Critical exponents for 3D O(n)-symmetric model with n > 3

TL;DR

This paper estimates critical exponents for 3D O(n) models with n>3 using six-loop RG expansions, showing resummation is unnecessary for large n and assessing the 1/n-expansion's accuracy.

Contribution

It provides new high-precision estimates of critical exponents for large n and analyzes the applicability of resummation techniques and the 1/n-expansion.

Findings

Resummation becomes unnecessary for n > 28 with 0.01 accuracy.

Critical exponents are accurately estimated for n > 3.

The 1/n-expansion is validated for n ≥ 28.

Abstract

Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location g_c and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An analysis of the numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy of about 0.01 is adopted as satisfactory for g_c and critical exponents. Further, results of the calculations performed are used to estimate the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to play the role of the lower boundary of the domain where this approximation provides high-precision estimates for the critical exponents.