Five-loop numerical evaluation of critical exponents of the $\phi^4$ theory - INSPIRE

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Five-loop numerical evaluation of critical exponents of the $\phi^4$ theory

Sep 22, 2013

8 pages

Part of Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013) : Beijing, China, May 16-21, 2013

Published in:

J.Phys.Conf.Ser. 523 (2014) 012049

Contribution to:

- ACAT 2013

Published: 2014

e-Print:

1309.5621 [cond-mat.stat-mech]

DOI:

10.1088/1742-6596/523/1/012049

View in:

ADS Abstract Service

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Abstract: (arXiv)

We present a new approach to calculation of anomalous dimensions in the framework of

\epsilon

-expansion and renormalization group method. This approach allows one to skip the calculation of renormalization constants and express anomalous dimensions in terms of renormalized diagrams, which are presented in a form suitable for numerical calculations. This approach can be easily automated and extended to a wide range of models. The power of this approach is illustrated on 5 loop calculations of beta-function and anomalous dimensions in

\phi^4

model.

Note:

8 pages, 5 figures. To be submitted to the proceedings of ACAT 2013

phi**n model: 4
anomalous dimension
numerical calculations
renormalization
beta function
critical phenomena

References(21)

Figures(0)

[1]

The field theoretic renormalization group in critical behavior theory and stochastic dynamics

A.N. Vasilev
(
- St. Petersburg State U.
)

- Boca Raton, USA: Chapman & Hall/CRC (2004) 681 p

[2]

Quantum field theory and critical phenomena

Jean Zinn-Justin
(
- Saclay
)

- Int.Ser.Monogr.Phys. 113 (2002) 1-1054

[3]

Critical properties of phi**4-theories

- River Edge, USA: World Scientific (2001) 489 p

[4]

New Approach to Evaluation of Multiloop Feynman Integrals: The Gegenbauer Polynomial x Space Technique

- Nucl.Phys.B 174 (1980) 345-377
•
DOI:
- 10.1016/0550-3213(80)90289-8

[5]

Five Loop Calculations in the $g \phi^4$ Model and the Critical Index $\eta$

- Phys.Lett.B 99 (1981) 147,
- Phys.Lett.B 101 (1981) 457 (erratum)
•
DOI:
- 10.1016/0370-2693(81)90968-0

[6]

A theorem on analytical calculability of 4-loop renormalization group functions

F.V. Tkachov
(
- Moscow, INR
)

- Phys.Lett.B 100 (1981) 65-68
•
DOI:
- 10.1016/0370-2693(81)90288-4

[6]

Integration by parts: The algorithm to calculate $\beta$ -functions in 4 loops

K.G. Chetyrkin
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Nucl.Phys.B 192 (1981) 159-204,
- Nucl. Phys. B192 ( 1981) 159-204
•
DOI:
- 10.1016/0550-3213(81)90199-1

[7]

INFRARED R OPERATION AND ULTRAVIOLET COUNTERTERMS IN THE MS SCHEME

K.G. Chetyrkin
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Phys.Lett.B 114 (1982) 340-344
•
DOI:
- 10.1016/0370-2693(82)90358-6

[7]

R* OPERATION CORRECTED

K.G. Chetyrkin
(
- Moscow, INR
)
,
Vladimir A. Smirnov
(
- Moscow State U.
)

- Phys.Lett.B 144 (1984) 419-424,
- IN *TBILISI 1984, PROCEEDINGS, QUARKS 84, VOL. 2* 112-122.
•
DOI:
- 10.1016/0370-2693(84)91291-7

[8]

Five Loop Renormalization Group Calculations in the $g \phi^4$ in Four-dimensions Theory

- Phys.Lett.B 132 (1983) 351
•
DOI:
- 10.1016/0370-2693(83)90324-6

[8]

THE METHOD OF UNIQUENESS, A NEW POWERFUL TECHNIQUE FOR MULTILOOP CALCULATIONS

D.I. Kazakov
(
- Dubna, JINR
)

- Phys.Lett.B 133 (1983) 406-410
•
DOI:
- 10.1016/0370-2693(83)90816-X

[8]

CALCULATION OF FEYNMAN INTEGRALS BY THE METHOD OF 'UNIQUENESS'

D.I. Kazakov
(
- Dubna, JINR
)

- Theor.Math.Phys. 58 (1984) 223-230,
- Teor.Mat.Fiz. 58 (1984) 343-353
•
DOI:
- 10.1007/BF01018044

[9]

Five loop renormalization group functions of O(n) symmetric phi4 theory and epsilon expansions of critical exponents up to epsilon5

H. Kleinert
(
- Freie U., Berlin
)
,
J. Neu
(
- Freie U., Berlin
)
,
V. Schulte-Frohlinde
(
- Freie U., Berlin
)
,
K.G. Chetyrkin
(
- Moscow, INR
)
,
S.A. Larin
(
- Moscow, INR
)

- Phys.Lett.B 272 (1991) 39-44,
- Phys.Lett.B 319 (1993) 545 (erratum)
•
e-Print:
- hep-th/9503230
•
DOI:
- 10.1016/0370-2693(91)91009-K

[10]

Critical dynamics: a field-theoretical approach

R. Folk
(
- Linz U.
)
,
Hans-Guenther Moser
(
- Salzburg U.
)

- J.Phys.A 39 (2006) R207-R313
•
DOI:
- 10.1088/0305-4470/39/24/R01

[11]

2011

Adzhemyan L. Ts
,
Kompaniets M. V

- Theor.Math.Phys. 169 (2011) 1450

[12]

2013

Adzhemyan L. Ts
,
Kompaniets M. V
,
Novikov S. V
,
Sazonov V. K

- Theor.Math.Phys. 175 (2013) 719

[13]

Renormalized quantum field theory

O.I. Zavyalov
(
- Lebedev Inst.
)

- Dordrecht, Netherlands: Kluwer (1990) 524 p. (Mathematics and its applications. Soviet series, 21)

[14]

An automatized algorithm to compute infrared divergent multiloop integrals

T. Binoth
(
- Annecy, LAPTH
)
,
G. Heinrich
(
- Orsay, LPT
)

- Nucl.Phys.B 585 (2000) 741-759
•
e-Print:
- hep-ph/0004013
•
DOI:
- 10.1016/S0550-3213(00)00429-6

[15]

Hepp and Speer Sectors within Modern Strategies of Sector Decomposition

A.V. Smirnov
(
- Moscow, Computing Ctr.
)
,
V.A. Smirnov
(
- SINP, Moscow
)

- JHEP 05 (2009) 004
•
e-Print:
- 0812.4700
•
DOI:
- 10.1088/1126-6708/2009/05/004

[16]

Inversion of the R Operation and $\Xi$ Functional

Grigorii B. Pivovarov
(
- Moscow, INR
)
,
F.V. Tkachov
(
- Moscow, INR
)

- Theor.Math.Phys. 77 (1988) 1038-1044,
- Teor.Mat.Fiz. 77 (1988) 51-59
•
DOI:
- 10.1007/BF01028678

[17]

of Guelf Report,1977

Nickel B
,
Meiron D
,
Baker G. Preprint University

- http://users.physik.fu-berlin.de/~kleinert/nickel/guelph.pdf