Vacuum expectation values from a variational approach

In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator. As an example we estimate the VEV's of all (UV regular) primary operators of the Ising model and of some of the Tricritical Ising Model conformal field theories when perturbed by any choice of the relevant primary operators. We compare our results with some other independent predictions.

Note:

LaTeX file, 11 pages. Revised Version Report-no: SPhT-t97/055;GEF-TH-97/5

11.25.Hf
11.15.Bt
11.80.Fv
Conformal field theories
Variational methods
Truncated Conformal Space Approach
Perturbation theory
I.R. divergences
Operator Product Expansion
field theory: conformal

References(41)

Figures(0)

Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

A.A. Belavin
(
- Landau Inst.
)
,
Alexander M. Polyakov
(
- Landau Inst.
)
,
A.B. Zamolodchikov
(
- CERN and
- Landau Inst.
)

- Nucl.Phys.B 241 (1984) 333-380,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 5-52. (NUCL. PHYS. B241 (1984) 333-380) AND CERN GENEVA - TH. 3827 (84,REC.JUN.) 71 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0550-3213(84)90052-X

Exact solutions of conformal field theory in two-dimensions and critical phenomena

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- Rev.Math.Phys. 1 (1990) 197-234,
- Also in *Rasetti, M.G. (ed): New problems, methods and techniques in quantum field theory and statistical mechanics* 55-92
•
DOI:
- 10.1142/S0129055X89000110

Integrable field theory from conformal field theory

A.B. Zamolodchikov
(
- Landau Inst.
)

- Adv.Stud.Pure Math. 19 (1989) 641-674

Integrals of Motion in Scaling Three State Potts Model Field Theory

A.B. Zamolodchikov
(
- Landau Inst.
)

- Int.J.Mod.Phys.A 3 (1988) 743-750,
- Also in *Itzykson, C. (ed.) et al.: Conformal invariance and applications to statistical mechanics* 705-712
•
DOI:
- 10.1142/S0217751X88000333

Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models

- Annals Phys. 120 (1979) 253-291,
- Also in *Jimbo, M. (ed.): Yang-Baxter equation in integrable systems* 82-120, and in *Rebbi, C. (ed.), Soliani, G. (ed.): Solitons and Particles*, 446-484,
•
DOI:
- 10.1016/0003-4916(79)90391-9

Off critical statistical models: Factorized scattering theories and bootstrap program

Giuseppe Mussardo
(
- SISSA, Trieste
)

- Phys.Rept. 218 (1992) 215-379
•
DOI:
- 10.1016/0370-1573(92)90047-4

Universal properties of selfavoiding walks from two-dimensional field theory

John L. Cardy
(
- UC, Santa Barbara
)
,
G. Mussardo
(
- SISSA, Trieste and
- INFN, Trieste
)

- Nucl.Phys.B 410 (1993) 451-493
•
e-Print:
- hep-th/9306028
•
DOI:
- 10.1016/0550-3213(93)90525-T

- J.Statist.Phys. 48 449

Perturbation Theory of Higher Spin Conserved Currents Off Criticality

Andrea Cappelli
(
- Bohr Inst.
)
,
Jose I. Latorre
(
- Barcelona U.
)

- Nucl.Phys.B 340 (1990) 659-691
•
DOI:
- 10.1016/0550-3213(90)90463-N

Perturbative Evaluation of the Conformal Anomaly at New Critical Points with Applications to Random Systems

A.W.W. Ludwig
(
- UC, Santa Barbara
)
,
John L. Cardy
(
- UC, Santa Barbara
)

- Nucl.Phys.B 285 (1987) 687-718
•
DOI:
- 10.1016/0550-3213(87)90362-2

Off Critical Point by Perturbation: The Ising Model Spin Spin Correlator

V.S. Dotsenko
(
- Landau Inst.
)

- Nucl.Phys.B 314 (1989) 687-706
•
DOI:
- 10.1016/0550-3213(89)90413-6

Nonlagrangian models of current algebra

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Phys.Rev. 179 (1969) 1499-1512
•
DOI:
- 10.1103/PhysRev.179.1499

- J.Phys.A 8 710

- Phys.Rev.Lett. 32 473

On Infrared Divergences

G. Parisi
(
- Ecole Normale Superieure
)

- Nucl.Phys.B 150 (1979) 163-172,
- Also in *Parisi, G.: Field theory, disorder and simulations* 153-162, and in *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 455-464
•
DOI:
- 10.1016/0550-3213(79)90298-0