597 research outputs found
Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory
For an anisotropic euclidean -theory with two interactions [u
(\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4] the -functions are
calculated from five-loop perturbation expansions in
dimensions, using the knowledge of the large-order behavior and Borel
transformations. For , an infrared stable cubic fixed point for
is found, implying that the critical exponents in the magnetic phase
transition of real crystals are of the cubic universality class. There were
previous indications of the stability based either on lower-loop expansions or
on less reliable Pad\'{e approximations, but only the evidence presented in
this work seems to be sufficently convincing to draw this conclusion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.htm
Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
We extend previous work on applying the epsilon-expansion to universal
properties of a cold, dilute Fermi gas in the unitary regime of infinite
scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential
to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in
epsilon=4-d, where d is the number of spatial dimensions. We also explore the
nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure
Large-Order Behavior of Two-coupling Constant -Theory with Cubic Anisotropy
For the anisotropic [u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N
\phi_i^4]-theory with {} we calculate the imaginary parts of the
renormalization-group functions in the form of a series expansion in , i.e.,
around the isotropic case. Dimensional regularization is used to evaluate the
fluctuation determinants for the isotropic instanton near the space dimension
4. The vertex functions in the presence of instantons are renormalized with the
help of a nonperturbative procedure introduced for the simple g{\phi^4-theory
by McKane et al.Comment: LaTeX file with eps files in src. See also
http://www.physik.fu-berlin.de/~kleinert/institution.htm
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
Duality between Topologically Massive and Self-Dual models
We show that, with the help of a general BRST symmetry, different theories in
3 dimensions can be connected through a fundamental topological field theory
related to the classical limit of the Chern-Simons model.Comment: 13 pages, LaTe
Spin Frustration and Orbital Order in Vanadium Spinels
We present the results of our theoretical study on the effects of geometrical
frustration and the interplay between spin and orbital degrees of freedom in
vanadium spinel oxides VO ( = Zn, Mg or Cd). Introducing an
effective spin-orbital-lattice coupled model in the strong correlation limit
and performing Monte Carlo simulation for the model, we propose a reduced spin
Hamiltonian in the orbital ordered phase to capture the stabilization mechanism
of the antiferromagnetic order. Orbital order drastically reduces spin
frustration by introducing spatial anisotropy in the spin exchange
interactions, and the reduced spin model can be regarded as weakly-coupled
one-dimensional antiferromagnetic chains. The critical exponent estimated by
finite-size scaling analysis shows that the magnetic transition belongs to the
three-dimensional Heisenberg universality class. Frustration remaining in the
mean-field level is reduced by thermal fluctuations to stabilize a collinear
ordering.Comment: 4 pages, 4 figures, proceedings submitted to SPQS200
Critical Exponents of the pure and random-field Ising models
We show that current estimates of the critical exponents of the
three-dimensional random-field Ising model are in agreement with the exponents
of the pure Ising system in dimension 3 - theta where theta is the exponent
that governs the hyperscaling violation in the random case.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.
Quantum phase transitions in the J-J' Heisenberg and XY spin-1/2 antiferromagnets on square lattice: Finite-size scaling analysis
We investigate the critical parameters of an order-disorder quantum phase
transitions in the spin-1/2 Heisenberg and XY antiferromagnets on square
lattice. Basing on the excitation gaps calculated by exact diagonalization
technique for systems up to 32 spins and finite-size scaling analysis we
estimate the critical couplings and exponents of the correlation length for
both models. Our analysis confirms the universal critical behavior of these
quantum phase transitions: They belong to 3D O(3) and 3D O(2) universality
classes, respectively.Comment: 7 pages, 3 figure
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