Mean Field and Monte Carlo Studies of SU($N$) Chiral Models in Three-dimensions

SU( N ) chiral models defined on three-dimensional cubic lattices arestudied using mean field and Monte Carlo techniques. Mean field theory predicts first-order transitions for all finite N greater than two. The mean field estimates of the transition temperature and discontinuity of the order parameter are in good agreement with computer simulations for N = 3 and 4. The N → ∞ limit of mean field theory has a first-order phase transition.

LATTICE FIELD THEORY: THREE-DIMENSIONAL
SYMMETRY: CHIRAL
SYMMETRY: SU(N) X SU(N)
LATTICE FIELD THEORY: CRITICAL PHENOMENA
EXPANSION 1/N
APPROXIMATION: MEAN FIELD
SYMMETRY: SU(4) X SU(4)
SYMMETRY: SU(5) X SU(5)
SYMMETRY: SU(3) X SU(3)
SYMMETRY: SU(2) X SU(2)

References(16)

Figures(0)

An algorithm for the poles at dimension four in the dimensional regularization procedure

Gerard 't Hooft
(
- CERN
)

- Nucl.Phys.B 62 (1973) 444-460
•
DOI:
- 10.1016/0550-3213(73)90263-0

Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields

Alexander M. Polyakov
(
- Landau Inst.
)

- Phys.Lett.B 59 (1975) 79-81
•
DOI:
- 10.1016/0370-2693(75)90161-6

Reliable Perturbative Results for Strong Interactions?

H.David Politzer
(
- Harvard U.
)

- Phys.Rev.Lett. 30 (1973) 1346-1349,
- Also in *Mohapatra, R. N. (Ed.), Lai, C. H. (Ed.): Gauge Theories Of Fundamental Interactions*, 333-336, and in *Rebbi, C. (Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 237-240,
- In *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 243-246,
•
DOI:
- 10.1103/PhysRevLett.30.1346

Gauge Transitions in Gauge and Spin Lattice Systems

Alexander A. Migdal
(
- Landau Inst.
)

- Sov.Phys.JETP 42 (1975) 743,
- Zh.Eksp.Teor.Fiz. 69 (1975) 1457

Ultraviolet Behavior of Nonabelian Gauge Theories

David J. Gross
(
- Princeton U.
)
,
Frank Wilczek
(
- Princeton U.
)

- Phys.Rev.Lett. 30 (1973) 1343-1346,
- Also in *Rebbi, C. (Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 233-236,
•
DOI:
- 10.1103/PhysRevLett.30.1343

Impossibility of Spontaneously Breaking Local Symmetries

S. Elitzur
(
- Tel Aviv U.
)

- Phys.Rev.D 12 (1975) 3978-3982
•
DOI:
- 10.1103/PhysRevD.12.3978

Confinement and the Critical Dimensionality of Space-Time

Michael Creutz
(
- Brookhaven
)

- Phys.Rev.Lett. 43 (1979) 553-556,
- Phys.Rev.Lett. 43 (1979) 890 (erratum)
•
DOI:
- 10.1103/PhysRevLett.43.553

Large Dimension Expansions and Transition Patterns in Lattice Gauge Theories

J.M. Drouffe
(
- Saclay
)

- Phys.Rept. 67 (1980) 63
•
DOI:
- 10.1016/0370-1573(80)90080-0

Possible Third Order Phase Transition in the Large N Lattice Gauge Theory

D.J. Gross
(
- Princeton U.
)
,
Edward Witten
(
- Harvard U.
)

- Phys.Rev.D 21 (1980) 446-453,
- In *Brezin, E. (ed.), Wadia, S.R. (ed.): The large N expansion in quantum field theory and statistical physics* 584-591,
- Preprint - GROSS, D. J. (REC.AUG 79) 25p
•
DOI:
- 10.1103/PhysRevD.21.446