857 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
Obtaining Bounds on The Sum of Divergent Series in Physics
Under certain circumstances, some of which are made explicit here, one can
deduce bounds on the full sum of a perturbation series of a physical quantity
by using a variational Borel map on the partial series. The method is
illustrated by applying it to various examples, physical and mathematical.Comment: 33 pages, Journal Versio
High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model
We report measurements of the critical exponents of the classical
three-dimensional Heisenberg model on simple cubic lattices of size with
= 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long
single-cluster Monte Carlo simulations near the phase transition. We compute
high precision estimates of the critical coupling , Binder's parameter
\nu,\beta / \nu, \eta\alpha / \nu$,
using extensively histogram reweighting and optimization techniques that allow
us to keep control over the statistical errors. Measurements of the
autocorrelation time show the expected reduction of critical slowing down at
the phase transition as compared to local update algorithms. This allows
simulations on significantly larger lattices than in previous studies and
consequently a better control over systematic errors in finite-size scaling
analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript
file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first
version arrived incomplete due to mailer problems
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
On three dimensional bosonization
We discuss Abelian and non-Abelian three dimensional bosonization within the
path-integral framework. We present a systematic approach leading to the
construction of the bosonic action which, together with the bosonization recipe
for fermion currents, describes the original fermion system in terms of vector
bosons.Comment: 15 pages, LaTe
Decoupling Transformations in Path Integral Bosonization
We construct transformations that decouple fermionic fields in interaction
with a gauge field, in the path integral representation of the generating
functional. Those transformations express the original fermionic fields in
terms of non-interacting ones, through non-local functionals depending on the
gauge field. This procedure, holding true in any number of spacetime dimensions
both in the Abelian and non-Abelian cases, is then applied to the path integral
bosonization of the Thirring model in 3 dimensions. Knowledge of the decoupling
transformations allows us, contrarily to previous bosonizations, to obtain the
bosonization with an explicit expression of the fermion fields in terms of
bosonic ones and free fermionic fields. We also explain the relation between
our technique, in the two dimensional case, and the usual decoupling in 2
dimensions.Comment: 22 pages, Late
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