The field-theoretical renormalization-group approach is used to estimate the universal critical value $g_6^{*}$ of the renormalized sextic coupling constant for the two-dimensional Ising model. A four-loop perturbative expansion for $g_6$ is calculated and resummed by means of the Padé-Borel-Leroy technique. Under the optimal value of the shift parameter $b,$ providing the fastest convergence of the iteration procedure, the estimates $g_6^{*}=1.10,$ $g_6^{*}{/g}_4^{*2}=2.94\mathrm{}$ are obtained, which agree quite well with those deduced recently by Zinn, Lai, and Fisher [Phys. Rev. E 54, 1176 (1996)] from the high-temperature expansions.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevB.58.2395