2 research outputs found
Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
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.Comment: 18 pages, 4 figure
Universality classes of three-dimensional -vector model
We study the conditions under which the critical behavior of the
three-dimensional -vector model does not belong to the spherically
symmetrical universality class. In the calculations we rely on the
field-theoretical renormalization group approach in different regularization
schemes adjusted by resummation and extended analysis of the series for
renormalization-group functions which are known for the model in high orders of
perturbation theory. The phase diagram of the three-dimensional -vector
model is built marking out domains in the -plane where the model belongs to
a given universality class.Comment: 9 pages, 1 figur