Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings

Guida, Riccardo; Konishi, Kenichi; Suzuki, Hiroshi

doi:10.1006/aphy.1996.0066

Cited by 75 publications

(71 citation statements)

References 20 publications

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“…Our analysis of results, including the selection of the relevant optima, will follow closely those adopted in the applications which proved the convergence of this method for the anharmonic oscillator [21,22,23,24]. Some of the guidelines developed on those studies are essential for our present application.…”

Section: Numerical Results For the Temperature Shiftmentioning

confidence: 95%

“…Another advantage is that one does not have to worry about infrared divergences, since, during the formal evaluation of graphs, the LDE arbitrary parameter naturally acts as such before disappearing during the optimization process. Also, the fact that a convergence proof for the quantum mechanical analogue of the model considered here does exist [21,22,23,24] is an extra bonus.…”

Section: Discussionmentioning

confidence: 97%

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Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

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We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c ′′ 2 which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc = T0{1+c1an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where T0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c ′′ 2 = 101.4, c ′′ 2 = 98.2 and c ′′ 2 = 82.9. Our analytical results seem to support the recent Monte Carlo estimates c1 = 1.32 ± 0.02 and c ′′ 2 = 75.7 ± 0.4.

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Section: Numerical Results For the Temperature Shiftmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 97%

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

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“…The remarkable convergence of OPE in simple models was investigated in numerous works (Bellet et al, 1996a,b;Bender et al, 1994;Duncan and Jones, 1993;Guida et al, 1995Guida et al, , 1996. It was found that at high orders the convergence of partition function of simple integrals (similar to the "zero dimensional GL" studied in (Wilkin and Moore, 1993) ),…”

Section: Rate Of Convergence Of Optmentioning

confidence: 99%

“…We follow here the convergence proof of (Bellet et al, 1996a,b;Bender et al, 1994;Duncan and Jones, 1993;Guida et al, 1995Guida et al, , 1996. The basic idea is to construct a conformal map from the original coupling g to a coupling of bounded range and isolate a nonanalytic prefactor.…”

Section: Rate Of Convergence Of Optmentioning

confidence: 99%

Ginzburg-Landau theory of type II superconductors in magnetic field

2010

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Thermodynamics of type II superconductors in electromagnetic field based on the GinzburgLandau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor -normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high Tc materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg -Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose -Einstein condensate.

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“…It is considered as a sort of variational method [13,14,15,16,17,18]. It has been successfully applied to various models [19,20,21,22], and applications to matrix models were done in Refs. [23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Improved perturbation method and its application to the IIB matrix model

Aoyama

Shibusa

2006

Nuclear Physics B

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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 observable 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.

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Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings

Cited by 75 publications

References 20 publications

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Ginzburg-Landau theory of type II superconductors in magnetic field

Improved perturbation method and its application to the IIB matrix model

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