Five-loop renormalization-group expansions for two-dimensional Euclidean λφ theory

The renormalization-group functions of the two-dimensional nvector λφ4 model are calculated in the five-loop approximation. Perturbative series for the β-function and critical exponents are resummed by the Pade-Borel-Leroy techniques. An account for the five-loop term shifts the Wilson fixed point location only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = −1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. For the 2D Ising model, the estimate ω = 1.31(3) for the correction-to-scaling exponent is found that is close to the values resulting from the hightemperature expansions. The field-theoretical renormalization-group (RG) approach proved to be a powerful tool for calculating the critical exponents and other universal quantities of the basic three-dimensional (3D) models of phase transitions. Today, many-loop RG expansions for β-functions (six-loop), critical exponents (seven-loop), higher-order couplings (four-loop), etc. of the 3D O(n)symmetric and cubic models are known resulting in the high-precision numerical estimates for experimentally accessible quantities [1-7]. The main aim of this report is to elaborate further the field-theoretical RG technique, namely,