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 $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to $\beta^{29}$ 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, $V(x)=x^2/2-gx^4/4$. 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 $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics simulations using finite size scaling techniques yield $\nu=0.6723(3)[8]$ and $\eta=0.0381(2)[2]$, 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