Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

P. Calabrese; E. V. Orlov; D. V. Pakhnin; A. I. Sokolov

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Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

P. Calabrese·E. V. Orlov·D. V. Pakhnin·A. I. Sokolov

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Abstract

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.

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P. Calabrese, E. V. Orlov, D. V. Pakhnin, A. I. Sokolov. 2005-09-15. Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation. https://arxiv.org/abs/cond-mat/0509415

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