Hamiltonian cycles on a random three-coordinate lattice

Nuclear Physics B

Volumn 528, Issue 3, 1998, Pages 523-532

  Eynard, B ^a,b   Guitter, E ^b   Kristjansen, C ^c  

^a DURHAM UNIVERSITY   (United Kingdom)

^b Centre National de la Recherche Scientifique   (France)

^c UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Hamiltonian cycle; O(n) model; Random lattice; Self avoiding walk

Indexed keywords

EID: 0032555845     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00391-5     Document Type: Article

References (28)

1. [1] M. Gordon, P. Kapadia and A. Malakis, J. Phys. A: Math. Gen. 9 (1976) 751; P.D. Gujrati, J. Phys. A: Math. Gen. 13 (1980) L437; T.G. Schmalz, G.E. Hite and D.J. Klein, J. Phys. A: Math. Gen. 17 (1984) 445; J. Suzuki and T. Izuyama, J. Phys. Soc. Jpn. 57 (1988) 818.
2. [1] M. Gordon, P. Kapadia and A. Malakis, J. Phys. A: Math. Gen. 9 (1976) 751; P.D. Gujrati, J. Phys. A: Math. Gen. 13 (1980) L437; T.G. Schmalz, G.E. Hite and D.J. Klein, J. Phys. A: Math. Gen. 17 (1984) 445; J. Suzuki and T. Izuyama, J. Phys. Soc. Jpn. 57 (1988) 818.
3. [1] M. Gordon, P. Kapadia and A. Malakis, J. Phys. A: Math. Gen. 9 (1976) 751; P.D. Gujrati, J. Phys. A: Math. Gen. 13 (1980) L437; T.G. Schmalz, G.E. Hite and D.J. Klein, J. Phys. A: Math. Gen. 17 (1984) 445; J. Suzuki and T. Izuyama, J. Phys. Soc. Jpn. 57 (1988) 818.
4. [1] M. Gordon, P. Kapadia and A. Malakis, J. Phys. A: Math. Gen. 9 (1976) 751; P.D. Gujrati, J. Phys. A: Math. Gen. 13 (1980) L437; T.G. Schmalz, G.E. Hite and D.J. Klein, J. Phys. A: Math. Gen. 17 (1984) 445; J. Suzuki and T. Izuyama, J. Phys. Soc. Jpn. 57 (1988) 818.
5. [2] P.W. Kasteleyn, Physica (Utrecht) 29 (1963) 1329.
6. [3] E.H. Lieb, Phys. Rev. Lett. 18 (1967) 692.
7. [4] J. Suzuki, J. Phys. Soc. Jpn. 57 (1988) 687.
8. [5] M.T. Batchelor, J. Suzuki and C.M. Yung, Phys. Rev. Lett. 73 (1994) 2646.
9. [6] H. Orland, C. Itzykson and C. de Dominics, J. Phys. Lett. 46 (1985) L-353.
10. [7] S. Higuchi, A field theoretic approach to the counting problem of Hamiltonian cycles of graphs, cond-mat/9711152.
11. [8] H.W.J. Blöte and B. Nienhuis, Phys. Rev. Lett. 72 (1994) 1372.
12. [9] A. Kast, Correlation length and average loop length of the fully packed loop model, cond-mat/9411132.
13. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
14. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
15. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
16. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
17. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
18. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
19. [10] I. Kostov, Mod. Phys. Lett. A 4 (1989) 217; M. Gaudin and I. Kostov, Phys. Lett. B 220 (1989) 200; B. Dupfantier and I. Kostov, Phys. Rev. Lett. 61 (1988) 1433; I. Kostov and M. Staudacher, Nucl. Phys. B 384 (1992) 459; B. Eynard and J. Zinn-Justin, Nucl. Phys. B 386 (1992) 55; B. Eynard and C. Kristjansen, Nucl. Phys. B 455 (1995) 577; B 483 [FS] (1997) 535.
20. [11] B. Eynard and C. Kristjansen, Nucl. Phys. B 466 (1996) 463.
21. [12] B. Eynard and C. Kristjansen, Nucl. Phys. B 516 (1998) 529.
22. [13] R.J. Baxter, J. Math. Phys. 11 (1970) 784.
23. [14] G. Cicuta, L. Molinari and E. Montaldi, Phys. Lett. B 306 (1993) 245; L. Chekhov and C. Kristjansen, Nucl. Phys. B 479 (1996) 683.
24. [14] G. Cicuta, L. Molinari and E. Montaldi, Phys. Lett. B 306 (1993) 245; L. Chekhov and C. Kristjansen, Nucl. Phys. B 479 (1996) 683.
25. [15] E.R. Hansen, A Table of Series and Products (Prentice-Hall, Engelwood Cliffs, NJ, 1975).
26. [16] B. Duplantier and I. Kostov, Nucl. Phys. B 340 (1990) 491.
27. [17] E. Brezin, C. Itzykson, G. Parisi and J.B. Zuber, Comm. Math. Phys. 59 (1978) 35.
28. [18] P. Di Francesco, B. Eynard and E. Guitter, Nucl. Phys. B 516 (1998) 543.