34 research outputs found
On stability of the three-dimensional fixed point in a model with three coupling constants from the expansion: Three-loop results
The structure of the renormalization-group flows in a model with three
quartic coupling constants is studied within the -expansion method up
to three-loop order. Twofold degeneracy of the eigenvalue exponents for the
three-dimensionally stable fixed point is observed and the possibility for
powers in to appear in the series is investigated.
Reliability and effectiveness of the -expansion method for the given
model is discussed.Comment: 14 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57
(1998
Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
The critical thermodynamics of the two-dimensional N-vector cubic and MN
models is studied within the field-theoretical renormalization-group (RG)
approach. The beta functions and critical exponents are calculated in the
five-loop approximation and the RG series obtained are resummed using the
Borel-Leroy transformation combined with the generalized Pad\'e approximant and
conformal mapping techniques. For the cubic model, the RG flows for various N
are investigated. For N=2 it is found that the continuous line of fixed points
running from the XY fixed point to the Ising one 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 the cubic model with
N\geq 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. For the quenched dilute
O(M) models ( models with N=0) the results are compatible with a stable
pure fixed point for M\geq1. For the MN model with M,N\geq2 all the
non-perturbative results are reproduced. In addition a new stable fixed point
is found for moderate values of M and N.Comment: 26 pages, 3 figure
The stability of a cubic fixed point in three dimensions from the renormalization group
The global structure of the renormalization-group flows of a model with
isotropic and cubic interactions is studied using the massive field theory
directly in three dimensions. The four-loop expansions of the \bt-functions
are calculated for arbitrary . The critical dimensionality and the stability matrix eigenvalues estimates obtained on the basis of
the generalized Pad-Borel-Leroy resummation technique are shown
to be in a good agreement with those found recently by exploiting the five-loop
\ve-expansions.Comment: 18 pages, LaTeX, 5 PostScript figure
Critical behavior of three-dimensional magnets with complicated ordering from three-loop renormalization-group expansions
The critical behavior of a model describing phase transitions in 3D
antiferromagnets with 2N-component real order parameters is studied within the
renormalization-group (RG) approach. The RG functions are calculated in the
three-loop order and resummed by the generalized Pade-Borel procedure
preserving the specific symmetry properties of the model. An anisotropic stable
fixed point is found to exist in the RG flow diagram for N > 1 and lies near
the Bose fixed point; corresponding critical exponents are close to those of
the XY model. The accuracy of the results obtained is discussed and estimated.Comment: 10 pages, LaTeX, revised version published in Phys. Rev.
Critical behavior of certain antiferromagnets with complicated ordering: Four-loop \ve-expansion analysis
The critical behavior of a complex N-component order parameter
Ginzburg-Landau model with isotropic and cubic interactions describing
antiferromagnetic and structural phase transitions in certain crystals with
complicated ordering is studied in the framework of the four-loop
renormalization group (RG) approach in (4-\ve) dimensions. By using
dimensional regularization and the minimal subtraction scheme, the perturbative
expansions for RG functions are deduced and resummed by the Borel-Leroy
transformation combined with a conformal mapping. Investigation of the global
structure of RG flows for the physically significant cases N=2 and N=3 shows
that the model has an anisotropic stable fixed point governing the continuous
phase transitions with new critical exponents. This is supported by the
estimate of the critical dimensionality obtained from six loops
via the exact relation established for the complex and real
hypercubic models.Comment: LaTeX, 16 pages, no figures. Expands on cond-mat/0109338 and includes
detailed formula
Randomly dilute Ising model: A nonperturbative approach
The N-vector cubic model relevant, among others, to the physics of the
randomly dilute Ising model is analyzed in arbitrary dimension by means of an
exact renormalization-group equation. This study provides a unified picture of
its critical physics between two and four dimensions. We give the critical
exponents for the three-dimensional randomly dilute Ising model which are in
good agreement with experimental and numerical data. The relevance of the cubic
anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio
Critical behavior of disordered systems with replica symmetry breaking
A field-theoretic description of the critical behavior of weakly disordered
systems with a -component order parameter is given. For systems of an
arbitrary dimension in the range from three to four, a renormalization group
analysis of the effective replica Hamiltonian of the model with an interaction
potential without replica symmetry is given in the two-loop approximation. For
the case of the one-step replica symmetry breaking, fixed points of the
renormalization group equations are found using the Pade-Borel summing
technique. For every value , the threshold dimensions of the system that
separate the regions of different types of the critical behavior are found by
analyzing those fixed points. Specific features of the critical behavior
determined by the replica symmetry breaking are described. The results are
compared with those obtained by the -expansion and the scope of the
method applicability is determined.Comment: 18 pages, 2 figure