Condensed Matter Physics, 2005, vol. 8, No. 1(41), p. 193-211, English

Title: Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
Authors: P.Calabrese (Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy) , E.V.Orlov, D.V.Pakhnin, A.I.Sokolov (Department of Physical Electronics, Saint Petersburg Electrotechnical University, Professor Popov Street 5, St. Petersburg 197376, Russia)

The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The β functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pad\'e-Borel-Leroy and conformal mapping techniques. It is found that for N=2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both β functions closer to each other. For N≥ 3 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N=0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.

Key words: renormalization group expansions, 2D cubic model
PACS: 75.10.Hk, 05.70.Jk, 64.60.Fr, 11.10.Kk

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