Universal effective coupling constants for the generalized Heisenberg model

The aim of this study is to find universal critical values of the dimensionless effective coupling constant $g_6$ and refined universal values $g_4$ for Heisenberg ferromagnets with $n$-component order parameters. These constants appear in the equation of state and determine the nonlinear susceptibilities $χ_4$ and $χ_6$ in the critical region. The sextic coupling $g_6$ is calculated as a function of $g_4$ in the three-loop approximation, the series obtained is resummed by the Pade-Borel method and then by substituting the Wilson fixed point coordinate $g_4^*$ into resultant expression numerical values of $g_6^*$ are obtained for different $n$. The numbers $g_4^*$ were determined from the six-loop expansions for $β$ function resummed using Borel-transformation-based techniques. The analysis of the accuracy of these $g_6^*$ values showed that they differ from the true values by no more than 1.6 %. The values of $g_6^*$ thus found were compared also with those given by the $1/n$ method what allowed to estimate the level of accuracy of this method.

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