Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

Kleinert, H.; Bossche, Bruno Van Den

doi:10.1103/physreve.63.056113

Cited by 21 publications

(19 citation statements)

References 71 publications

(401 reference statements)

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“…5 and 19 of the textbooks [29,18], respectively; improving perturbation theory by a variational principle goes back at least to [30]). Accurate critical exponents [18,27,28] and amplitude ratios [31] have been obtained. For a truncated partial sum through u r L−2 of Eq.…”

Section: Resummation and Resultsmentioning

confidence: 98%

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

Kastening

2004

Phys. Rev. A

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For an O͑N͒-symmetric scalar field theory with Euclidean action ͐d 3 x ͓ 1 2 ͉ ٌ ͉ 2 + 1 2 r 2 + 1 4! u 4 ͔ , where = ͑ 1 , . . . , N ͒ is a vector of N real-field components, variational perturbation theory through seven loops is employed for N =0,1,2,3,4 to compute the renormalized value of r / ͑N +2͒u 2 at the phase transition. Its exact large-N limit is determined as well. We also extend an earlier computation of the interaction-induced shift ⌬͗ 2 ͘ / Nu from N =1,2,4 to N =0,3. For N = 2, the results for the two quantities are used to compute the second-order shift of the condensation temperature of a dilute Bose gas, both in the homogenous case and for the wide limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo simulations for N =1,2,4. The Appendix contains previously unpublished numerical seven-loop data.

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Section: Resummation and Resultsmentioning

confidence: 98%

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

Kastening

2004

Phys. Rev. A

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“…[17]. In 4 − ε dimensions with ε-expansion, this has not even been done for the simpler O(N )-symmetric φ 4 -model without gauge field.…”

Section: Discussionmentioning

confidence: 99%

Two-loop effective potential of O(N)-symmetric scalar QED in 4−ε dimensions

Kleinert¹,

Bossche²

2002

Nuclear Physics B

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The effective potential of scalar QED is computed analytically up to two loops in the Landau gauge. The result is given in 4 − ε dimensions using minimal subtraction and ε-expansions. In three dimensions (ε = 1), our calculation is intended to help throw light on unsolved problems of the superconducting phase transition, where critical exponents and the position of the tricritical point have not yet found a satisfactory explanation within the renormalization group approach.

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“…(24) of Kleinert and Van den Bossche [2]. For a given , the optimal value of û B Ã ͑͒ is now determined by…”

Section: Eq (91)mentioning

confidence: 99%

Erratum: Minimal renormalization without ε-expansion: Four-loop free energy in three dimensions for general n above and below T_{c} [Phys. Rev. E 67, 056115 (2003)]

Strösser¹,

Dohm²

2004

Phys. Rev. E

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Recently it has been shown by Chen and Dohm [1] that, within a ͑d , n͒ universality class, two-scale factor universality in the form of our Eq. (11) is valid only for isotropic systems and systems with cubic symmetry. For anisotropic systems of noncubic symmetry in the same ͑d , n͒ universality class, our Eq. (11) must be replaced by Eq. (3) of Chen and Dohm [1].On the right-hand side (rhs) of Eq. (91) the term +͑n −1͒ 880 3 Li 2 ͑ − 1 3 ͒ should be added, thus the term + 8803 Li 2 ͑ − 1 3 ͒ should be included in the curly brackets of

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Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

Cited by 21 publications

References 71 publications

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

Two-loop effective potential of O(N)-symmetric scalar QED in 4−ε dimensions

Erratum: Minimal renormalization without ε-expansion: Four-loop free energy in three dimensions for general n above and below T_{c} [Phys. Rev. E 67, 056115 (2003)]

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