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

TL;DR

This paper investigates the critical behavior of the two-dimensional N-vector cubic model using five-loop renormalization-group calculations, revealing how fixed points shift with loop order and N, and clarifying the nature of criticality for different N values.

Contribution

The study provides five-loop RG calculations for the 2D N-vector cubic model, clarifying fixed point structures and their N-dependence, and resolving ambiguities from lower-order approximations.

Findings

For N=2, the fixed points form a continuous line well captured by resummed series.

For N>2, five-loop terms shift the cubic fixed point towards the Ising fixed point.

Results support that the cubic fixed point for N>2 is an artifact of perturbation theory.

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.