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An iterative solution of the three-colour problem on a random lattice

B. Eynard
(
- Durham U.
)
,
C. Kristjansen
(
- Copenhagen U.
)

1998

14 pages

Published in:

Nucl.Phys.B 516 (1998) 529-542

e-Print:

cond-mat/9710199 [cond-mat]

DOI:

10.1016/S0550-3213(98)00042-X

Report number:

DTP-97-55

View in:

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Abstract: (Elsevier)

We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and critical behaviour of the resulting matrix model. Based on a set of loop equations we develop an algorithm which enables us to solve the three-colour problem recursively.

Note:

14 pages, LaTeX, misprints corrected, approximation of (6.20) refined Report-no: DTP-97-55, SPhT-97/122, NBI-HE-97-51 Subj-class: Statistical Mechanics Journal-ref: Nucl. Phys. B516 (1998) 529

04.60.Nc
05.20.y
Three-colour problem
O ( n ) model
Random lattices
2D quantum gravity
O( n) model
quantum gravity
symmetry: O(N)
dimension: 2

References(16)

Figures(0)

Duality Relations and Equivalences for Models With O( $N$ ) and Cubic Symmetry

E. Domany
(
- Weizmann Inst.
)
,
D. Mukamel
(
- IBM Watson Res. Ctr.
)
,
B. Nienhuis
(
- Washington U., Seattle
)
,
A. Schwimmer
(
- Imperial Coll., London
)

- Nucl.Phys.B 190 (1981) 279-287
•
DOI:
- 10.1016/0550-3213(81)90559-9

O( $n$ ) Vector Model on a Planar Random Lattice: Spectrum of Anomalous Dimensions

I.K. Kostov
(
- Saclay, SPhT
)

- Mod.Phys.Lett.A 4 (1989) 217,
•
DOI:
- 10.1142/S0217732389000289

O(n) MODEL ON A FLUCTUATING PLANAR LATTICE: SOME EXACT RESULTS

M. Gaudin
(
- Saclay, SPhT
)
,
I. Kostov
(
- Saclay, SPhT
)

- Phys.Lett.B 220 (1989) 200-206
•
DOI:
- 10.1016/0370-2693(89)90037-3

Conformal Spectra of Polymers on a Random Surface

Bertrand Duplantier
(
- Saclay
)
,
Ivan Kostov
(
- Saclay
)

- Phys.Rev.Lett. 61 (1988) 1433
•
DOI:
- 10.1103/PhysRevLett.61.1433

Multicritical phases of the O(n) model on a random lattice

Ivan K. Kostov
(
- Saclay
)
,
Matthias Staudacher
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 384 (1992) 459-483
•
e-Print:
- hep-th/9203030
•
DOI:
- 10.1016/0550-3213(92)90576-W

The O(n) model on a random surface: Critical points and large order behavior

B. Eynard
(
- Saclay
)
,
Jean Zinn-Justin
(
- Saclay
)

- Nucl.Phys.B 386 (1992) 558-591
•
e-Print:
- hep-th/9204082
•
DOI:
- 10.1016/0550-3213(92)90630-T

Exact solution of the O(n) model on a random lattice

B. Eynard
(
- Saclay
)
,
C. Kristjansen
(
- Saclay
)

- Nucl.Phys.B 455 (1995) 577-618
•
e-Print:
- hep-th/9506193
•
DOI:
- 10.1016/0550-3213(95)00469-9

More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n| > 2

B. Eynard
(
- Saclay
)
,
C. Kristjansen
(
- NORDITA
)

- Nucl.Phys.B 466 (1996) 463-487
•
e-Print:
- hep-th/9512052
•
DOI:
- 10.1016/0550-3213(96)00104-6

Phase structure of the O(n) model on a random lattice for n > 2

B. Durhuus
(
- Copenhagen U.
)
,
C. Kristjansen
(
- Nordita
)

- Nucl.Phys.B 483 (1997) 535-551
•
e-Print:
- hep-th/9609008
•
DOI:
- 10.1016/S0550-3213(96)00574-3

Vertex models on Feynman diagrams

D.A. Johnston
(
- Heriot-Watt U.
)
,
P. Plechac
(
- Oxford U.
)

- Phys.Lett.A 248 (1998) 37-48
•
e-Print:
- hep-lat/9709003
•
DOI:
- 10.1016/S0375-9601(98)00651-3

Matrix models and graph coloring

Giovanni M. Cicuta
(
- Bari U. and
- INFN, Bari
)
,
Luca Molinari
(
- Milan U. and
- INFN, Milan
)
,
Emilio Montaldi
(
- Milan U. and
- INFN, Milan
)

- Phys.Lett.B 306 (1993) 245-251
•
DOI:
- 10.1016/0370-2693(93)90075-S

Hermitian matrix model with plaquette interaction

L. Chekhov
(
- Steklov Math. Inst., Moscow
)
,
C. Kristjansen
(
- Nordita
)

- Nucl.Phys.B 479 (1996) 683-696
•
e-Print:
- hep-th/9605013
•
DOI:
- 10.1016/0550-3213(96)00382-3

Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of space-time

- Phys.Lett.B 306 (1993) 19-26
•
e-Print:
- hep-th/9302133
•
DOI:
- 10.1016/0370-2693(93)91131-6

Construction of noncritical string field theory by transfer matrix formalism in dynamical triangulation

Yoshiyuki Watabiki
(
- INS, Tokyo
)

- Nucl.Phys.B 441 (1995) 119-166
•
e-Print:
- hep-th/9401096
•
DOI:
- 10.1016/0550-3213(95)00010-P

The Two point function of c = -2 matter coupled to 2-D quantum gravity

- Nucl.Phys.B 504 (1997) 555-579
•
e-Print:
- hep-th/9705202
•
DOI:
- 10.1016/S0550-3213(97)00525-7

Planar Diagrams

- Commun.Math.Phys. 59 (1978) 35
•
DOI:
- 10.1007/BF01614153