Critical thermodynamics of the two-dimensional systems in five-loop renormalization-group approximation

The RG functions of the 2D n-vector λφ4 model are calculated in the five-loop approximation. Perturbative series for the β-function and critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy techniques, resummation procedures are optimized and an accuracy of the numerical results is estimated. In the Ising case n = 1 as well as in the others (n = 0, n = −1, n = 2, 3, ...32) an account for the five-loop term is found to shift the Wilson fixed point location only briefly, leaving it outside the segment formed by the results of the corresponding lattice calculations; even error bars of the RG and lattice estimates do not overlap in the most cases studied. This is argued to reflect the influence of the singular (non-analytical) contribution to the β-function that can not be found perturbatively. The evaluation of the critical exponents for n = 1, n = 0 and n = −1 in the five-loop approximation and comparison of the numbers obtained with their known exact counterparts 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 value 4/3 resulting from the conformal invariance. What follows is the radically shortened version of the paper written in Russian. It contains all the formulas, tables and complete list of references of the original paper. The full-scale text (18 preprint style pages) is available as a Russified LaTeX file or PostScript file; they may be delivered electronically by request. Please, contact the corresponding author using his e-address: [email protected]. The Hamiltonian of the model describing the critical behavior of various two-dimensional systems reads: H = ∫