VARIATIONAL APPROACH TO HAMILTONIAN LATTICE THEORIES

Horn, D.

doi:10.1103/PhysRevD.23.1824

VARIATIONAL APPROACH TO HAMILTONIAN LATTICE THEORIES

D. Horn
(
- Tel Aviv U.
)

Jul, 1980

24 pages

Published in:

Phys.Rev.D 23 (1981) 1824

DOI:

10.1103/PhysRevD.23.1824

Report number:

TAUP 859-80

View in:

reference search9 citations

Citations per year

Abstract: (APS)

A variational calculation of the vacuum energy of a Hamiltonian lattice theory is formulated in terms of a finite box Hamiltonian for a cluster of points. The box Hamiltonian contains surface terms which are proportional to order parameters of the system. It is tested on the Ising model and applied to Z(N) spin models in 1 + 1 and 2 + 1 dimensions. Z(3) is found to have an exceptional phase-transition structure. The application of the method to local gauge theories is discussed.

STATISTICAL MECHANICS: ISING
LATTICE FIELD THEORY
GAUGE FIELD THEORY: Z(N)
GAUGE FIELD THEORY: TWO-DIMENSIONAL
GAUGE FIELD THEORY: THREE-DIMENSIONAL
STATISTICAL MECHANICS: CRITICAL PHENOMENA
GAUGE FIELD THEORY: Z(3)
FIELD THEORY: VACUUM STATE
APPROXIMATION: MEAN FIELD
NUMERICAL CALCULATIONS

References(14)

Figures(0)

The one-dimensional Ising model with a transverse field

Pierre Pfeuty

- Annals Phys. 57 (1970) 1, 79-90
•
DOI:
- 10.1016/0003-4916(70)90270-8

Order and Disorder in Gauge Systems and Magnets

Eduardo H. Fradkin
(
- SLAC
)
,
Leonard Susskind
(
- SLAC and
- Tel Aviv U.
)

- Phys.Rev.D 17 (1978) 2637
•
DOI:
- 10.1103/PhysRevD.17.2637

- J.Phys.C 4 2370

HAMILTONIAN APPROACH TO Z(N) LATTICE GAUGE THEORIES

- Phys.Rev.D 19 (1979) 3715
•
DOI:
- 10.1103/PhysRevD.19.3715

Renormalization, vortices, and symmetry breaking perturbations on the two-dimensional planar model

Jorge V. Jose
(
- Brown U.
)
,
Leo P. Kadanoff
(
- Brown U.
)
,
Scott Kirkpatrick
(
- SUNY, Stony Brook and
- IBM Watson Res. Ctr.
)
,
David R. Nelson
(
- Harvard U.
)

- Phys.Rev.B 16 (1977) 1217-1241
•
DOI:
- 10.1103/PhysRevB.16.1217

The Phase Structure of Discrete Abelian Spin and Gauge Systems

- Phys.Rev.D 19 (1979) 3698
•
DOI:
- 10.1103/PhysRevD.19.3698

Monte Carlo Study of Abelian Lattice Gauge Theories

- Phys.Rev.D 20 (1979) 1915,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 182-189. ( Phys. Rev. D20 ( 1979) 1915-1922) and Brookhaven Nat. Lab. Upton - BNL-26307 (79,REC.SEP.) 36p
•
DOI:
- 10.1103/PhysRevD.20.1915

Dual Variables for Lattice Gauge Theories and the Phase Structure of Z(N) Systems

- Phys.Rev.D 21 (1980) 1013
•
DOI:
- 10.1103/PhysRevD.21.1013

- Phys.Rev.Lett. 43 799

Discrete and Abelian Lattice Gauge Theories

Michael B. Green
(
- Oxford U.
)

- Nucl.Phys.B 144 (1978) 473-512
•
DOI:
- 10.1016/0550-3213(78)90382-6

Phase Diagrams of Lattice Gauge Theories with Higgs Fields

Eduardo H. Fradkin
(
- SLAC and
- Stanford U., Phys. Dept.
)
,
Stephen H. Shenker
(
- Cornell U., LNS
)

- Phys.Rev.D 19 (1979) 3682-3697
•
DOI:
- 10.1103/PhysRevD.19.3682

Gauge and Matter Screening in a $Z$ (2) Theory

D. Horn
(
- Tel Aviv U.
)
,
S. Yankielowicz
(
- Tel Aviv U.
)

- Phys.Lett.B 85 (1979) 347-352
•
DOI:
- 10.1016/0370-2693(79)91269-3

Variational Approach to the $Z$ (2) Gauge Theory

D. Horn
(
- Tel Aviv U.
)
,
E. Katznelson
(
- Tel Aviv U.
)

- Phys.Lett.B 91 (1980) 397-400
•
DOI:
- 10.1016/0370-2693(80)91005-9

Phase Diagrams for Coupled Spin Gauge Systems

Michael Creutz
(
- Brookhaven
)

- Phys.Rev.D 21 (1980) 1006,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 481-487. ( Phys. Rev. D21 ( 1980) 1006-1012) and Brookhaven Nat. Lab. Upton - BNL-26587 (79,REC.SEP.) 30p
•
DOI:
- 10.1103/PhysRevD.21.1006