TY - JOUR

T1 - Pseudo-ε expansion and renormalized coupling constants at criticality

AU - Sokolov, A.I.

AU - Nikitina, M.A.

PY - 2014

Y1 - 2014

N2 - Universal values of dimensional effective coupling constants g2k that determine nonlinear susceptibilities χ2k and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ε expansion approach. Pseudo-ε expansions for g6 and g8 at criticality are derived for arbitrary n. Analogous series for ratios R6=g6/g42 and R8=g8/g43 that figure in the equation of state are also found, and the pseudo-ε expansion for Wilson fixed point location g4* descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0≤n≤64, with the most attention paid to the physically important cases n=0,1,2,3. Pseudo-ε expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g4* and R6* that are almost as accurate as those provided by th

AB - Universal values of dimensional effective coupling constants g2k that determine nonlinear susceptibilities χ2k and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ε expansion approach. Pseudo-ε expansions for g6 and g8 at criticality are derived for arbitrary n. Analogous series for ratios R6=g6/g42 and R8=g8/g43 that figure in the equation of state are also found, and the pseudo-ε expansion for Wilson fixed point location g4* descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0≤n≤64, with the most attention paid to the physically important cases n=0,1,2,3. Pseudo-ε expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g4* and R6* that are almost as accurate as those provided by th

U2 - 10.1103/PhysRevE.89.052127

DO - 10.1103/PhysRevE.89.052127

M3 - Article

VL - 89

SP - 052127_1-10

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

ER -