arXiv:1312.1062v2 [cond-mat.stat-mech] 26 Feb 2014 Critical Exponents in Two Dimensions and Pseudo-ǫ Expansion M. A. Nikitina and A. I. Sokolov * Department of Quantum Mechanics, Saint Petersburg State University, Ulyanovskaya 1, Petergof, Saint Petersburg, 198504 Russia (Dated: February 27, 2014) Abstract The critical behavior of two-dimensional n-vector λφ 4 field model is studied within the frame- work of pseudo-ǫ expansion approach. Pseudo-ǫ expansions for Wilson fixed point location g * and critical exponents originating from five-loop 2D renormalization group series are derived. Numer- ical estimates obtained within Pad´ e and Pad´ e-Borel resummation procedures as well as by direct summation are presented for n = 1, n = 0 and n = −1, i. e. for the models which are exactly solvable. The pseudo-ǫ expansions for g * , critical exponents γ and ν have small lower-order coef- ficients and slow increasing higher-order ones. As a result, direct summation of these series with optimal cut off provides numerical estimates that are no worse than those given by the resumma- tion approaches mentioned. This enables one to consider the pseudo-ǫ expansion technique itself as some specific resummation method. PACS numbers: 05.10.Cc, 05.70.Jk, 64.60.ae, 64.60.Fr 1