Nonanalyticity of the Callan-Symanzik Beta function of two-dimensional O(N) models

Calabrese, Pasquale; Caselle, Michele; Celi, Alessio; Pelissetto, Andrea; Vicari, Ettore

doi:10.1088/0305-4470/33/46/301

Nonanalyticity of the Callan-Symanzik Beta function of two-dimensional O(N) models

Pasquale Calabrese
(
- Pisa U.
)
,
Michele Caselle
(
- Turin U. and
- INFN, Turin
)
,
Alessio Celi
(
- Pisa U.
)
,
Andrea Pelissetto
(
- Rome U. and
- INFN, Rome
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

May, 2000

17 pages

Published in:

J.Phys.A 33 (2000) 8155-8170

e-Print:

hep-th/0005254 [hep-th]

DOI:

10.1088/0305-4470/33/46/301

Report number:

DFTT-21-2000,
IFUP-TH-2000-16

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Abstract:

We discuss the analytic properties of the Callan-Symanzik beta-function beta(g) associated with the zero-momentum four-point coupling g in the two-dimensional phi^4 model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behavior of beta(g) at the fixed point g^*. We argue that beta'(g) = beta'(g^*) + O(|g-g^*|^{1/7}) for N=1 and beta'(g) = beta'(g^*) + O(1/\log |g-g^*|) for N > 2. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi^4 theory. We discuss how these nonanalytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.

Note:

18 pages. Discussion on Logarithmic CFT added in Appendix A. References updated. A note on the interpretation of the p_5 constant added. Final version, accepted for publication in Journal of Physics A Report-no: DFTT 21/2000, IFUP-TH/2000-16

phi**n model: 4
dimension: 2
symmetry: O(N)
renormalization group: beta function
analytic properties
asymptotic behavior
Ising model
critical phenomena
Borel transformation
field theory: conformal

References(62)

Figures(0)

- J.Statist.Phys. 23 49

Ising Model Critical Indices in Three-Dimensions from the Callan-Symanzik Equation

G.A. Baker
(
- Los Alamos and
- Brookhaven and
- Guelph U. and
- Temple U. and
- MIT, LNS
)
,
B.G. Nickel
(
- Los Alamos and
- Brookhaven and
- Guelph U. and
- Temple U. and
- MIT, LNS
)
,
M.S. Green
(
- Los Alamos and
- Brookhaven and
- Guelph U. and
- Temple U. and
- MIT, LNS
)
,
D.I. Meiron
(
- Los Alamos and
- Brookhaven and
- Guelph U. and
- Temple U. and
- MIT, LNS
)

- Phys.Rev.Lett. 36 (1976) 1351-1354,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 520-523. (Phys. Rev. Lett. 36 (1976) 1351-1354). (see Book Index)
•
DOI:
- 10.1103/PhysRevLett.36.1351

Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation

George A. Baker, Jr.
(
- Saclay and
- Los Alamos
)
,
Bernie G. Nickel
(
- Guelph U.
)
,
Daniel I. Meiron
(
- MIT
)

- Phys.Rev.B 17 (1978) 1365-1374
•
DOI:
- 10.1103/PhysRevB.17.1365

Critical thermodynamics of the two-dimensional systems in five loop renormalization group approximation

e-Print:
- hep-th/0003140

Divergence of the Perturbation Theory Series and the Quasiclassical Theory

L.N. Lipatov
(
- St. Petersburg, INP
)

- Sov.Phys.JETP 45 (1977) 216-223,
- Zh.Eksp.Teor.Fiz. 72 (1977) 411-427

Perturbation Theory at Large Order. 1. The phi**2N Interaction

E. Brezin
(
- Saclay
)
,
J.C. Le Guillou
(
- Paris U., VI-VII
)
,
Jean Zinn-Justin
(
- Saclay
)

- Phys.Rev.D 15 (1977) 1544-1557,
- Also in *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 91-104
•
DOI:
- 10.1103/PhysRevD.15.1544

- Phys.Rev.D 15 1588

Critical Exponents for the N Vector Model in Three-Dimensions from Field Theory

J.C. Le Guillou
(
- Paris U., VI-VII
)
,
Jean Zinn-Justin
(
- Saclay
)

- Phys.Rev.Lett. 39 (1977) 95-98,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 527-530. (Phys. Rev. Lett. 39 (1977) 95-98). (see Book Index)
•
DOI:
- 10.1103/PhysRevLett.39.95

Critical Exponents from Field Theory

J.C. Le Guillou
(
- Paris U., VI-VII
)
,
Jean Zinn-Justin
(
- Saclay
)

- Phys.Rev.B 21 (1980) 3976-3998,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 531-553. (Phys. Rev. B21 (1980) 3976-3998). (see Book Index)
•
DOI:
- 10.1103/PhysRevB.21.3976