Universal critical coupling constants for the three-dimensional n-vector model from field theory

TL;DR

This paper uses field theory and renormalization group techniques to estimate universal critical coupling constants g_6 and g_8 for the three-dimensional O(n) model, providing highly accurate numerical values for a wide range of n.

Contribution

It presents new high-precision estimates of critical coupling constants g_6 and g_8 for the 3D O(n) model using advanced resummation of RG series, extending results to n=40.

Findings

Accurate estimates of g_6^*(n) for n=1 to 40 with less than 0.3% error.

Consistent estimates of g_8^* with RG equations and epsilon-expansion for n > 8.

Demonstrates the effectiveness of Pade-Borel-Leroy resummation in critical coupling calculations.

Abstract

The field-theoretical renormalization group approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and g_8 are calculated in the four-loop and three-loop approximations respectively and then resummed by means of the Pade-Borel-Leroy technique. Under the optimal value of the shift parameter b providing the fastest convergence of the iteration procedure numerical estimates for the universal critical values g_6^*(n) are obtained for n = 1, 2, 3,...40 with the accuracy no worse than 0.3%. The RG expansion for g_8 demonstrates stronger divergence and results in considerably cruder numerical estimates. They are found to be consistent with the values of g_8^* deduced from the exact RG equations and, for n > 8, with those given by a constrained analysis of corresponding \epsilon-expansion.