Renormalized sextic coupling constant for the two-dimensional Ising model from field theory

TL;DR

This paper uses field-theoretical renormalization group methods and four-loop perturbative expansions to estimate the universal sextic coupling constant for the 2D Ising model, providing results consistent with previous high-temperature expansion studies.

Contribution

It presents the first four-loop perturbative calculation of the sextic coupling constant for the 2D Ising model using resummation techniques, improving the accuracy of universal critical value estimates.

Findings

Estimated g_6^* = 1.10 for the 2D Ising model

Found g_6^*/(g_4^*)^2 = 2.94, aligning with previous results

Demonstrated the effectiveness of Pade-Borel-Leroy resummation in critical phenomena

Abstract

The field-theoretical renormalization group approach is used to estimate the universal critical value g_6^* of renormalized sextic coupling constant for the two-dimensional Ising model. Four-loop perturbative expansion for g_6 is calculated and 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 the estimates g_6^* = 1.10, g_6^*/{g_4^*}^2 = 2.94 are obtained which agree quite well with those deduced recently by S.-Y. Zinn, S.-N. Lai, and M. E. Fisher (Phys. Rev. E 54 (1996) 1176) from the high-temperature expansions.