Critical Ising Correlation Functions in the Plane and on the Torus

Di Francesco, P.; Saleur, H.; Zuber, J.B.

doi:10.1016/0550-3213(87)90202-1

Critical Ising Correlation Functions in the Plane and on the Torus

Jul 1, 1987

55 pages

Published in:

Nucl.Phys.B 290 (1987) 527

Published: 1987

DOI:

10.1016/0550-3213(87)90202-1

Report number:

SACLAY-SPH-T-87-097

View in:

AMS MathSciNet

reference search114 citations

Citations per year

Abstract: (Elsevier)

Explicit expressions are given for all correlation functions of spin, disorder and energy operators of the critical Ising model in the plane or on the torus. Formulae for insertions of energy-momentum tensors may also be written, giving access to correlation functions of secondary fields. Two alternative methods are used throughout the paper: bosonization of the fermion representation of the Ising model or use of the free field (orbifold) interpretation of the Ashkin-Teller model. Many identities result from the consistency between these alternative approaches.

STATISTICAL MECHANICS: ISING
CORRELATION FUNCTION
TENSOR: ENERGY-MOMENTUM
STATISTICAL MECHANICS: BOSONIZATION
MODEL: ASHKIN-TELLER
SPACE-TIME: TORUS
SPACE-TIME: ORBIFOLD

References(29)

Figures(0)

Two-dimensional Ising model as a soluble problem of many fermions

T.D. Schultz
(
- IBM Watson Res. Ctr.
)
,
D.C. Mattis
(
- IBM Watson Res. Ctr.
)
,
Elliott H. Lieb
(
- Yeshiva U.
)

- Rev.Mod.Phys. 36 (1964) 856-871
•
DOI:
- 10.1103/RevModPhys.36.856

ISING FERMIONS. 1. TWO-DIMENSIONS

C. Itzykson
(
- Saclay
)

- Nucl.Phys.B 210 (1982) 448-476
•
DOI:
- 10.1016/0550-3213(82)90173-0

Quantum Field Theory and the Two-Dimensional Ising Model

J.B. Zuber
(
- Harvard U.
)
,
C. Itzykson
(
- Saclay
)

- Phys.Rev.D 15 (1977) 2875
•
DOI:
- 10.1103/PhysRevD.15.2875

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Bernard Nienhuis
(
- Philips Research Labs, Eindhoven
)

- J.Statist.Phys. 34 (1984) 731-761
•
DOI:
- 10.1007/BF01009437

Correlation functions on the critical lines of the Baxter and Ashkin-Teller models

Leo P. Kadanoff
,
Alan C. Brown
(
- Brown U.
)

- Annals Phys. 121 (1979) 318-342
•
DOI:
- 10.1016/0003-4916(79)90100-3

RENORMALIZATION CONNECTION BETWEEN THE EIGHT VERTEX MODEL AND THE GAUSSIAN MODEL

H.J.F. Knops
(
- Nijmegen U.
)

- Annals Phys. 128 (1980) 448-462
•
DOI:
- 10.1016/0003-4916(80)90328-0

- Phys.Rev.B 24 5229

Conformal and Current Algebras on General Riemann Surface

Tohru Eguchi
(
- Tokyo U.
)
,
Hirosi Ooguri
(
- Tokyo U.
)

- Nucl.Phys.B 282 (1987) 308-328,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 814-834. (NUCL. PHYS. B282 (1987) 308-328) AND TOKYO UNIV. - UT-491 (86,REC.SEP.) 33 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(87)90686-9

- Phys.Rev.B 3 3819

Chiral Bosonization on Riemann Surface

Tohru Eguchi
(
- Ecole Normale Superieure
)
,
Hirosi Ooguri
(
- Tokyo U.
)

- Phys.Lett.B 187 (1987) 127,
•
DOI:
- 10.1016/0370-2693(87)90084-0

Calculation of critical exponents in two-dimensions from quantum field theory in one-dimension

A. Luther
(
- Harvard U.
)
,
I. Peschel
(
- Harvard U.
)

- Phys.Rev.B 12 (1975) 3908-3917
•
DOI:
- 10.1103/PhysRevB.12.3908

The Quantum Sine-Gordon Equation as the Massive Thirring Model

Sidney R. Coleman
(
- Harvard U.
)

- Phys.Rev.D 11 (1975) 2088,
•
DOI:
- 10.1103/PhysRevD.11.2088

Soliton Operators for the Quantized Sine-Gordon Equation

S. Mandelstam
(
- UC, Berkeley
)

- Phys.Rev.D 11 (1975) 3026,
•
DOI:
- 10.1103/PhysRevD.11.3026

Two-Dimensional Conformal Invariant Theories on a Torus

C. Itzykson
(
- Saclay
)
,
J.B. Zuber
(
- Saclay
)

- Nucl.Phys.B 275 (1986) 580-616
•
DOI:
- 10.1016/0550-3213(86)90576-6

Conformal Invariance, the Central Charge, and Universal Finite Size Amplitudes at Criticality

- Phys.Rev.Lett. 56 (1986) 742-745,
- Phys. Rev. Lett. 56 ( 1986) 742-745
•
DOI:
- 10.1103/PhysRevLett.56.742

Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly

Ian Affleck
(
- Princeton U.
)

- Phys.Rev.Lett. 56 (1986) 746-748,
- Phys. Rev. Lett. 56 ( 1986) 746-748,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 277-279. (PHYS. REV. LETT. 56 (1986) 746-748) AND PREPRINT - AFFLECK, I. (REC.MAR.86) 7 P. (SEE BOOK INDEX),
- IN *CARDY, J.L. (ED.): FINITE-SIZE SCALING* 347-349. (PHYS. REV. LETT. 56 (1986) 746-748) AND PREPRINT - AFFLECK, I. (REC.MAR.86) 7 P. (SEE BOOK INDEX)
•
DOI:
- 10.1103/PhysRevLett.56.746

Operator Content of Two-Dimensional Conformally Invariant Theories

John L. Cardy
(
- UC, Santa Barbara
)

- Nucl.Phys.B 270 (1986) 186-204,
- Also in *Goddard, P. (ed.), Olive, D. (ed.): KAC-MOODY AND VIRASORO ALGEBRAS* 461-479
•
DOI:
- 10.1016/0550-3213(86)90552-3

Heterotic String Theory. 1. The Free Heterotic String

- Nucl.Phys.B 256 (1985) 253,
- In *Schellekens, A.N. (ed.): Superstring construction* 76-107. (Nucl. Phys. B256 (1985) 253-284) and Preprint - Gross, D.J. (85,rec.Apr.) 58 p. (see Book Index)
•
DOI:
- 10.1016/0550-3213(85)90394-3

Derivation of extended scaling relations between critical exponents in two-dimensional models from the one-dimensional Luttinger model

M.P.M. den Nijs
(
- Illinois U., Chicago
)

- Phys.Rev.B 23 (1981) 6111-6125
•
DOI:
- 10.1103/PhysRevB.23.6111

Conformal Invariance and the Spectrum of the {} Chain

- Phys.Rev.Lett. 58 (1987) 771
•
DOI:
- 10.1103/PhysRevLett.58.771

- Phys.Lett.B 185 832

- J.Phys.Soc.Jap. 53 147

- J.Phys.Soc.Jap. 53 153

- J.Phys.Soc.Jap. 53 183

Discrete Symmetries of Conformal Theories

J.B. Zuber
(
- Saclay
)

- Phys.Lett.B 176 (1986) 127,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 406-408. (PHYS. LETT. B176 (1986) 1270129)
•
DOI:
- 10.1016/0370-2693(86)90936-6

1-25 of 29
1
2
25 / page