83 research outputs found
Twisting cocycles in fundamental representation and triangular bicrossproduct Hopf algebras
We find the general solution to the twisting equation in the tensor bialgebra
of an associative unital ring viewed as that of
fundamental representation for a universal enveloping Lie algebra and its
quantum deformations. We suggest a procedure of constructing twisting cocycles
belonging to a given quasitriangular subbialgebra .
This algorithm generalizes Reshetikhin's approach, which involves cocycles
fulfilling the Yang-Baxter equation. Within this framework we study a class of
quantized inhomogeneous Lie algebras related to associative rings in a certain
way, for which we build twisting cocycles and universal -matrices. Our
approach is a generalization of the methods developed for the case of
commutative rings in our recent work including such well-known examples as
Jordanian quantization of the Borel subalgebra of and the null-plane
quantized Poincar\'e algebra by Ballesteros at al. We reveal the role of
special group cohomologies in this process and establish the bicrossproduct
structure of the examples studied.Comment: 20 pages, LaTe
Universal R-matrix for null-plane quantized Poincar{\'e} algebra
The universal --matrix for a quantized Poincar{\'e} algebra introduced by Ballesteros et al is evaluated. The solution is obtained
as a specific case of a formulated multidimensional generalization to the
non-standard (Jordanian) quantization of .Comment: 9 pages, LaTeX, no figures. The example on page 5 has been
supplemented with the full descriptio
On critical behavior of phase transitions in certain antiferromagnets with complicated ordering
Within the four-loop \ve expansion, we study the critical behavior of
certain antiferromagnets with complicated ordering. We show that an anisotropic
stable fixed point governs the phase transitions with new critical exponents.
This is supported by the estimate of critical dimensionality
obtained from six loops via the exact relation established
for the real and complex hypercubic models.Comment: Published versio
Extended jordanian twists for Lie algebras
Jordanian quantizations of Lie algebras are studied using the factorizable
twists. For a restricted Borel subalgebras of the
explicit expressions are obtained for the twist element , universal
-matrix and the corresponding canonical element . It is
shown that the twisted Hopf algebra is
self dual. The cohomological properties of the involved Lie bialgebras are
studied to justify the existence of a contraction from the Dinfeld-Jimbo
quantization to the jordanian one. The construction of the twist is generalized
to a certain type of inhomogenious Lie algebras.Comment: 28 pages, LaTe
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
New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop \epsilon expansions
A new approach to summation of divergent field-theoretical series is
suggested. It is based on the Borel transformation combined with a conformal
mapping and does not imply the exact asymptotic parameters to be known. The
method is tested on functions expanded in their asymptotic power series. It is
applied to estimating the critical exponent values for an N-vector field model,
describing magnetic and structural phase transitions in cubic and tetragonal
crystals, from five-loop \epsilon expansions.Comment: 9 pages, LaTeX, 3 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.
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