Universal effective coupling constant ratios of 3D scalar ϕ⁴ field theory and pseudo-ϵ expansion

E-ISSN： 2100-014x|125|issue|05001-05001

ISSN： 2100-014x

Source： EPJ Web of Conference, Vol.125, Iss.issue, 2016-10, pp. : 05001-05001

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Abstract

The ratios R_2k = g_2k/g^{k − 1}₄ of renormalized coupling constants g_2k entering the small-field equation of state approach universal values R*_2k at criticality. They are calculated for the three-dimensional λϕ⁴ field theory within the pseudo-ϵ expansion approach. Pseudo-ϵ expansions for R*₆, R*₈, R*₁₀ are derived in the five-loop approximation, numerical estimates are obtained with a help of the Padé–Borel–Leroy resummation technique. Its use gives R*₆ = 1.6488, the number which perfectly agrees with the most recent lattice result R*₆ = 1.649. For the octic coupling the pseudo-ϵ expansion is less favorable numerically. Nevertheless the Padé–Borel–Leroy resummation leads to the estimate R*₈ = 0.890 close to the values R*₈ = 0.87, R*₈ = 0.857 extracted from the lattice and field-theoretical calculations. The pseudo-ϵ expansion for R*₁₀ turns out to have big and rapidly increasing coefficients. This makes correspondent estimates strongly dependent on the Borel–Leroy shift parameter b and prevents proper evaluation of R*₁₀