Two-dimensional phase transition models and λϕ4 field theory

A. I. Sokolov
2006 Journal of Physical Studies  
An overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λφ 4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Padé-Borel-Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations.
more » ... e 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. The estimates obtained on the base of pseudo-expansions originating from the 5-loop 2D RG series are also discussed.
doi:10.30970/jps.10.351 fatcat:ftpu7y2eqra2bllgorcobrzkjy