Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-09-15
Condensed Matter Phys. 8 (2005) 193-211
Physics
Condensed Matter
Statistical Mechanics
18 pages, 4 figures
Scientific paper
The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pade-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 beta-functions closer to each another. For N > 2 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.
Calabrese Pasquale
Orlov E. V.
Pakhnin D. V.
Sokolov Aleksandr I.
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