6,971 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
Observing Quantum Tunneling in Perturbation Series
We apply Borel resummation method to the conventional perturbation series of
ground state energy in a metastable potential, . We observe
numerically that the discontinuity of Borel transform reproduces the imaginary
part of energy eigenvalue, i.e., total decay width due to the quantum
tunneling. The agreement with the exact numerical value is remarkable in the
whole tunneling regime 0.Comment: 12 pages, 2 figures. Phyzzx, Tables.tex, The final version to appear
in Phys. Lett.
Variational Perturbation Approach to Resonance-State Wave Functions
The variational perturbation theory for wave functions, which has been shown
to work well for bound states of the anharmonic oscillator, is applied to
resonance states of the anharmonic oscillator with negative coupling constant.
We obtain uniformly accurate wave functions starting from the bound states.Comment: 10 pages, RevTeX, 4 ps figures. There were some calculational
mistakes in the previous manuscript. The correct results obtained by our
method show excellent agreement with the exact solution
Self-energy and critical temperature of weakly interacting bosons
Using the exact renormalization group we calculate the momentum-dependent
self-energy Sigma (k) at zero frequency of weakly interacting bosons at the
critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D <
4. We obtain the complete crossover function interpolating between the critical
regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength
regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k)
\propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the
same footing with a reasonable estimate for the critical exponent eta in D=3.
From our Sigma (k) we find for the interaction-induced shift of T_c in three
dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave
scattering length and n is the density.Comment: 4 pages,1 figur
Improved Perturbation Method and its Application to the IIB Matrix Model
We present a new scheme for extracting approximate values in ``the improved
perturbation method'', which is a sort of resummation technique capable of
evaluating a series outside the radius of convergence. We employ the
distribution profile of the series that is weighted by nth-order derivatives
with respect to the artificially introduced parameters. By those weightings the
distribution becomes more sensitive to the ``plateau'' structure in which the
consistency condition of the method is satisfied. The scheme works effectively
even in such cases that the system involves many parameters. We also propose
that this scheme has to be applied to each observables separately and be
analyzed comprehensively.
We apply this scheme to the analysis of the IIB matrix model by the improved
perturbation method obtained up to eighth order of perturbation in the former
works. We consider here the possibility of spontaneous breakdown of Lorentz
symmetry, and evaluate the free energy and the anisotropy of space-time extent.
In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-
and SO(7)-symmetric vacua that have been observed. It is also found that there
are two distinct SO(4)-symmetric vacua that have almost the same value of free
energy but the extent of space-time is different. From the approximate values
of free energy, we conclude that the SO(4)-symmetric vacua are most preferred
among those three types of vacua.Comment: 52 pages, published versio
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
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
The Calculation of Critical Amplitudes in SU(2) Lattice Gauge Theory
We calculate the critical amplitudes of the Polyakov loop and its
susceptibility at the deconfinement transition of (3+1) dimensional SU(2) gauge
theory. To this end we study the corrections due to irrelevant exponents in the
scaling functions. As a guiding line for determining the critical amplitudes we
use envelope equations which we derive from the finite size scaling formulae of
the observables. We have produced new high precision data on N^3 x 4 lattices
for N=12,18,26 and 36. With these data we find different corrections to the
asymptotic scaling behaviour above and below the transition. Our result for the
universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and thus
in excellent agreement with a recent measurement for the 3d Ising model.Comment: 27 pages, 11 figures, Latex2
Optimized Perturbation Theory for Wave Functions of Quantum Systems
The notion of the optimized perturbation, which has been successfully applied
to energy eigenvalues, is generalized to treat wave functions of quantum
systems. The key ingredient is to construct an envelope of a set of
perturbative wave functions. This leads to a condition similar to that obtained
from the principle of minimal sensitivity. Applications of the method to
quantum anharmonic oscillator and the double well potential show that uniformly
valid wave functions with correct asymptotic behavior are obtained in the
first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure
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