6,676 research outputs found
Higher orders of the high-temperature expansion for the Ising model in three dimensions
The new algorithm of the finite lattice method is applied to generate the
high-temperature expansion series of the simple cubic Ising model to
for the free energy, to for the magnetic
susceptibility and to for the second moment correlation length.
The series are analyzed to give the precise value of the critical point and the
critical exponents of the model.Comment: Lattice2003(Higgs), 3 pages, 2 figure
New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions
We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of 26th order to 46th order in the inverse temperature. The
obtained series give the estimate of the critical exponent for the specific
heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter
High precision Monte Carlo study of the 3D XY-universality class
We present a Monte Carlo study of the two-component model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
and , where the statistical and
systematical errors are given in the first and second bracket, respectively.
These results are more precise than any previous theoretical estimate of the
critical exponents for the 3D XY universality class.Comment: 13 page
New Optimization Methods for Converging Perturbative Series with a Field Cutoff
We take advantage of the fact that in lambda phi ^4 problems a large field
cutoff phi_max makes perturbative series converge toward values exponentially
close to the exact values, to make optimal choices of phi_max. For perturbative
series terminated at even order, it is in principle possible to adjust phi_max
in order to obtain the exact result. For perturbative series terminated at odd
order, the error can only be minimized. It is however possible to introduce a
mass shift in order to obtain the exact result. We discuss weak and strong
coupling methods to determine the unknown parameters. The numerical
calculations in this article have been performed with a simple integral with
one variable. We give arguments indicating that the qualitative features
observed should extend to quantum mechanics and quantum field theory. We found
that optimization at even order is more efficient that at odd order. We compare
our methods with the linear delta-expansion (LDE) (combined with the principle
of minimal sensitivity) which provides an upper envelope of for the accuracy
curves of various Pade and Pade-Borel approximants. Our optimization method
performs better than the LDE at strong and intermediate coupling, but not at
weak coupling where it appears less robust and subject to further improvements.
We also show that it is possible to fix the arbitrary parameter appearing in
the LDE using the strong coupling expansion, in order to get accuracies
comparable to ours.Comment: 10 pages, 16 figures, uses revtex; minor typos corrected, refs. adde
Towards a fully automated computation of RG-functions for the 3- O(N) vector model: Parametrizing amplitudes
Within the framework of field-theoretical description of second-order phase
transitions via the 3-dimensional O(N) vector model, accurate predictions for
critical exponents can be obtained from (resummation of) the perturbative
series of Renormalization-Group functions, which are in turn derived
--following Parisi's approach-- from the expansions of appropriate field
correlators evaluated at zero external momenta.
Such a technique was fully exploited 30 years ago in two seminal works of
Baker, Nickel, Green and Meiron, which lead to the knowledge of the
-function up to the 6-loop level; they succeeded in obtaining a precise
numerical evaluation of all needed Feynman amplitudes in momentum space by
lowering the dimensionalities of each integration with a cleverly arranged set
of computational simplifications. In fact, extending this computation is not
straightforward, due both to the factorial proliferation of relevant diagrams
and the increasing dimensionality of their associated integrals; in any case,
this task can be reasonably carried on only in the framework of an automated
environment.
On the road towards the creation of such an environment, we here show how a
strategy closely inspired by that of Nickel and coworkers can be stated in
algorithmic form, and successfully implemented on the computer. As an
application, we plot the minimized distributions of residual integrations for
the sets of diagrams needed to obtain RG-functions to the full 7-loop level;
they represent a good evaluation of the computational effort which will be
required to improve the currently available estimates of critical exponents.Comment: 54 pages, 17 figures and 4 table
A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
We present a Monte Carlo study of the one-component model on the
cubic lattice in three dimensions. Leading order scaling corrections are
studied using the finite size scaling method. We compute the corrections to
scaling exponent with high precision. We determine the value of the
coupling at which leading order corrections to scaling vanish. Using
this result we obtain estimates for critical exponents that are more precise
than those obtained with field theoretic methods.Comment: 20 pages, two figures; numbers cited from ref. 23 corrected, few
typos correcte
Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion
We apply the linear delta expansion to the quantum mechanical version of the
slow rollover transition which is an important feature of inflationary models
of the early universe. The method, which goes beyond the Gaussian
approximation, gives results which stay close to the exact solution for longer
than previous methods. It provides a promising basis for extension to a full
field theoretic treatment.Comment: 12 pages, including 4 figure
Critical Exponents from Five-Loop Strong-Coupling phi^4-Theory in 4- epsilon Dimensions
With the help of strong-coupling theory, we calculate the critical exponents
of O(N)-symmetric phi^4-theories in 4- epsilon dimensions up to five loops with
an accuracy comparable to that achieved by Borel-type resummation methods.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
For many physical quantities, theory supplies weak- and strong-coupling
expansions of the types and \alpha ^p\sum b_n
(\alpha^{-2/q) ^n, respectively. Either or both of these may have a zero
radius of convergence. We present a simple interpolation algorithm which
rapidly converges for an increasing number of known expansion coefficients. The
accuracy is illustrated by calculating the ground state energies of the
anharmonic oscillator using only the leading large-order coefficient
(apart from the trivial expansion coefficent ). The errors are less
than 0.5 for all g. The algorithm is applied to find energy and mass of the
Fr\"ohlich-Feynman polaron. Our mass is quite different from Feynman's
variational approach.Comment: PostScript, http://www.physik.fu-berlin.de/kleinert.htm
Dynamic surface scaling behavior of isotropic Heisenberg ferromagnets
The effects of free surfaces on the dynamic critical behavior of isotropic
Heisenberg ferromagnets are studied via phenomenological scaling theory,
field-theoretic renormalization group tools, and high-precision computer
simulations. An appropriate semi-infinite extension of the stochastic model J
is constructed, the boundary terms of the associated dynamic field theory are
identified, its renormalization in d <= 6 dimensions is clarified, and the
boundary conditions it satisfies are given. Scaling laws are derived which
relate the critical indices of the dynamic and static infrared singularities of
surface quantities to familiar static bulk and surface exponents. Accurate
computer-simulation data are presented for the dynamic surface structure
factor; these are in conformity with the predicted scaling behavior and could
be checked by appropriate scattering experiments.Comment: 9 pages, 2 figure
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