A generalized Beraha conjecture for non-planar graphs

Nuclear Physics B

Volumn 875, Issue 3, 2013, Pages 678-718

  Jacobsen, Jesper Lykke ^a,b   Salas, Jesús ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Beraha conjecture; Berker Kadanoff phase; Generalized Petersen graphs; Non planar graphs; Potts model; Transfer matrix

Indexed keywords

EID: 84883183336     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2013.07.012     Document Type: Article

References (61)

1. Appel K.I., Haken W. Illinois J. Math. 1977, 21:429-567.
2. Baxter R.J. J. Phys. C: Solid State Phys. 1973, 6:L445-L448.
3. Baxter R.J. Exactly Solved Models in Statistical Mechanics 1982, Academic Press, London-New York.
4. Baxter R.J. Proc. Roy. Soc. London A 1982, 383:43-54.
5. Baxter R.J. J. Phys. A: Math. Gen. 1986, 19:2821-2839.
6. Baxter R.J. J. Phys. A: Math. Gen. 1987, 20:5241-5261.
7. Baxter R.J., Temperley H.N.V., Ashley S.E. Proc. Roy. Soc. London A 1978, 358:535-559.
8. Bedini A., Jacobsen J.L. J. Phys. A: Math. Theor. 2010, 43:385001. arxiv:1003.4847.
9. Beraha S. Infinite non-trivial families of maps and chromials 1975, PhD thesis, John Hopkins University.
10. Beraha S., Kahane J. J. Combin. Theory Ser. B 1979, 27:1-12.
11. Beraha S., Kahane J., Weiss N.J. Proc. Nat. Acad. Sci. USA 1975, 72:4209.
12. Beraha S., Kahane J., Weiss N.J. Limits of zeroes of recursively defined families of polynomials. Advances in Mathematics Supplementary Studies 1978, vol. 1:213-232. Academic Press, New York. G.-C. Rota (Ed.).
13. Beraha S., Kahane J., Weiss N.J. J. Combin. Theory Ser. B 1980, 28:52-65.
14. Bini D.A., Fiorentino G. Numerical computation of polynomial roots using MPSolve version 2.2 software package and documentation available for download at. ftp://ftp.dm.unipi.it/pub/mpsolve/MPSolve-2.2.tgz.
15. Bini D.A., Fiorentino G. Num. Algorithms 2000, 23:127-173.
16. Birkhoff G.D., Lewis D.C. Trans. Amer. Math. Soc. 1946, 60:355-451.
17. Chang S.-C., Jacobsen J.L., Salas J., Shrock R. J. Stat. Phys. 2004, 114:763-823. arxiv:cond-mat/0211623.
18. Chang S.-C., Salas J., Shrock R. J. Stat. Phys. 2002, 107:1207-1253. arxiv:cond-mat/0108144.
19. Chang S.-C., Shrock R. Physica A 2001, 296:131-182. arxiv:cond-mat/0005232.
20. Chang S.-C., Shrock R. J. Stat. Phys. 2003, 112:815-879. arxiv:cond-mat/0205424.
21. Dasmahapatra S., Martin P. J. Phys. A: Math. Gen. 1996, 29:263.
22. Fortuin C.M., Kasteleyn P.W. Physica 1972, 57:536-564.
23. Guttmann A., Enting I.G. J. Phys. A 1994, 27:5801-5812. arxiv:hep-lat/9312083.
24. Halverson T., Ram A. Eur. J. Comb. 2005, 26:869-921. arxiv:math/0401314.
25. Jackson B. J. Geom. 2003, 76:95-109. arxiv:math/0205047.
26. Jacobsen J.L., Richard J.-F., Salas J. Nucl. Phys. B 2006, 743:153-206. arxiv:cond-mat/0511059.
27. Jacobsen J.L., Salas J. J. Stat. Phys. 2001, 104:701-723. arxiv:cond-mat/0011456.
28. Jacobsen J.L., Salas J. J. Stat. Phys. 2006, 122:705-760. arxiv:cond-mat/0407444.
29. Jacobsen J.L., Salas J. Nucl. Phys. B 2007, 783:238-296. arxiv:cond-mat/0703228.
30. Jacobsen J.L., Salas J. J. Combin. Theory B 2013, 103:532-565. arxiv:1009.4062.
31. Jacobsen J.L., Salas J., Sokal A.D. J. Stat. Phys. 2003, 112:921-1017. arxiv:cond-mat/0204587.
32. Jacobsen J.L., Saleur H. Nucl. Phys. B 2006, 743:207-248. arxiv:cond-mat/0512058.
33. Jacobsen J.L., Saleur H. J. Stat. Phys. 2008, 132:707-719. arxiv:0803.2665.
34. Jacobsen J.L., Scullard C.R. J. Phys. A: Math. Theor. 2012, 45:494003. arxiv:1205.0622.
35. Jacobsen J.L., Scullard C.R. J. Phys. A: Math. Theor. 2013, 46:075001. arxiv:1211.4335.
36. Jaeger F. Nowhere-zero flow problems. Selected Topics in Graph Theory 1988, vol. 3. Academic Press.
37. Janke W., Villanova R. Nucl. Phys. B 1997, 489:679-696. arxiv:hep-lat/9612008.
38. Oxley J., Welsh D. Combin. Probab. Comput. 2002, 11:403.
39. Pasquier V., Saleur H. Nucl. Phys. B 1990, 330:523-556.
40. Pasquier V., Saleur H. Nucl. Phys. B 1990, 330:523-556.
41. Potts R.B. Proc. Camb. Phil. Soc. 1952, 48:106-109.
42. Read N., Saleur H. Nucl. Phys. B 2001, 613:409. arxiv:hep-th/0106124.
43. Richard J.-F., Jacobsen J.L. Nucl. Phys. B 2006, 750:250-264. arxiv:math-ph/0605016.
44. Richard J.-F., Jacobsen J.L. Nucl. Phys. B 2007, 769:256-274. arxiv:math-ph/0608055.
45. Salas J., Shrock R. Phys. Rev. E 2001, 64:0111111. arxiv:cond-mat/0102190.
46. Salas J., Sokal A.D. J. Stat. Phys. 2001, 104:609-699. arxiv:cond-mat/0004330.
47. Salas J., Sokal A.D. J. Stat. Phys. 2009, 135:279-373. arxiv:0711.1738.
48. Salas J., Sokal A.D. J. Stat. Phys. 2011, 144:1028-1122. arxiv:1002.3761.
49. Saleur H. Comm. Math. Phys. 1990, 132:657-679.
50. Saleur H. Nucl. Phys. B 1991, 360:219-263.
51. Shrock R. Discrete Math. 2001, 231:421-446. arxiv:cond-mat/9908387.
52. Sokal A.D. Comb. Prob. Comp. 2001, 10:41-77. arxiv:cond-mat/9904146.
53. Sokal A.D. Comb. Prob. Comp. 2004, 13:221-261. arxiv:cond-mat/0012369.
54. Tutte W.T. Proc. London Math. Soc. 1950, 51:474-483.
55. Tutte W.T. Can. J. Math. 1954, 6:81-90.
56. Tutte W.T. Graph Theory 1984, Addison-Wesley, New York.
57. Watkins M.E. J. Combin. Theory 1969, 6:152-164.
58. Wu F.Y. Rev. Mod. Phys. 1982, 54:235-268.
59. Wu F.Y. Rev. Mod. Phys. 1983, 55:315. (Erratum).
60. Wu F.Y., Wang Y.K. J. Math. Phys. 1976, 17:439.
61. Zhang C.-Q. Integer Flows and Cycle Covers of Graphs 1997, Marcel Dekker, New York.