메뉴 건너뛰기




Volumn 104, Issue 3-4, 2001, Pages 609-699

Transfer matrices and partition-function zeros for antiferromagnetic potts models. I. General theory and square-lattice chromatic polynomial

Author keywords

Antiferromagnetic Potts model; Beraha numbers; Beraha Kahane Weiss theorem; Chromatic polynomial; Chromatic root; Fortuin Kasteleyn representation; Square lattice; Temperley Lieb algebra; Transfer matrix

Indexed keywords


EID: 0035430046     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010376605067     Document Type: Article
Times cited : (91)

References (147)
  • 2
  • 3
    • 0042492825 scopus 로고
    • F. Y. Wu, Rev. Mod. Phys. 54:235 (1982); 55:315 (E) (1983).
    • (1983) Rev. Mod. Phys. , vol.55
  • 19
    • 0032183370 scopus 로고    scopus 로고
    • cond-mat/9807105
    • R. Shrock and S.-H. Tsai, Physica A 259:315 (1998), cond-mat/9807105.
    • (1998) Physica A , vol.259 , pp. 315
    • Shrock, R.1    Tsai, S.-H.2
  • 21
    • 0032183105 scopus 로고    scopus 로고
    • cond-mat/9807107
    • S.-H. Tsai, Physica A 259:349 (1998), cond-mat/9807107.
    • (1998) Physica A , vol.259 , pp. 349
    • Tsai, S.-H.1
  • 22
  • 23
    • 0033101214 scopus 로고    scopus 로고
    • cond-mat/9811410
    • R. Shrock and S.-H. Tsai, Physica A 265:186 (1999), cond-mat/9811410.
    • (1999) Physica A , vol.265 , pp. 186
    • Shrock, R.1    Tsai, S.-H.2
  • 26
  • 28
    • 0346704344 scopus 로고    scopus 로고
    • cond-mat/9908323
    • R. Shrock, Phys. Lett. A 261:57 (1999), cond-mat/9908323.
    • (1999) Phys. Lett. A , vol.261 , pp. 57
    • Shrock, R.1
  • 29
    • 0035961996 scopus 로고    scopus 로고
    • cond-mat/9908387
    • R. Shrock, Discrete Math. 231:421 (2001), cond-mat/9908387.
    • (2001) Discrete Math. , vol.231 , pp. 421
    • Shrock, R.1
  • 30
    • 0033901002 scopus 로고    scopus 로고
    • cond-mat/9907403
    • R. Shrock and S.-H. Tsai, Physica A 275:429 (2000), cond-mat/9907403.
    • (2000) Physica A , vol.275 , pp. 429
    • Shrock, R.1    Tsai, S.-H.2
  • 31
    • 0034250847 scopus 로고    scopus 로고
    • cond-mat/0001389
    • R. Shrock, Physica A 283:388 (2000), cond-mat/0001389.
    • (2000) Physica A , vol.283 , pp. 388
    • Shrock, R.1
  • 33
  • 34
  • 45
    • 0000391398 scopus 로고
    • E. H. Lieb, at pp. 169-170
    • A. Lenard, cited in E. H. Lieb, Phys. Rev. 162:162 (1967) at pp. 169-170.
    • (1967) Phys. Rev. , vol.162 , pp. 162
    • Lenard, A.1
  • 52
    • 0035486418 scopus 로고    scopus 로고
    • Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
    • cond-mat/0101197, Oct.
    • J. Cardy, J.-L. Jacobsen, and A. D. Sokal, Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice, cond-mat/0101197, to appear in J. Stat. Phys. 105(1/2) (Oct. 2001).
    • (2001) J. Stat. Phys. , vol.105 , Issue.1-2
    • Cardy, J.1    Jacobsen, J.-L.2    Sokal, A.D.3
  • 63
    • 0007162822 scopus 로고    scopus 로고
    • private communications
    • C. L. Henley, private communications.
    • Henley, C.L.1
  • 69
    • 0007304486 scopus 로고
    • unpublished, circa
    • S. Beraha, unpublished, circa 1974.
    • (1974)
    • Beraha, S.1
  • 74
    • 0007229624 scopus 로고
    • D. R. Fulkerson ed., Studies in Mathematics #12 (Mathematical Association of America, Washington)
    • W. T. Tutte, in Studies in Graph Theory, Part II, D. R. Fulkerson ed., Studies in Mathematics #12 (Mathematical Association of America, Washington, 1975), pp. 361-377.
    • (1975) Studies in Graph Theory , Issue.PART II , pp. 361-377
    • Tutte, W.T.1
  • 82
    • 0007235404 scopus 로고
    • (Cambridge), H. Osborn, ed., NATO Advanced Science Institutes Series B: Physics #315 (Plenum, New York)
    • H. N. V. Temperley, in Low-Dimensional Topology and Quantum Field Theory (Cambridge, 1992), H. Osborn, ed., NATO Advanced Science Institutes Series B: Physics #315 (Plenum, New York, 1993), pp. 203-212.
    • (1992) Low-Dimensional Topology and Quantum Field Theory , pp. 203-212
    • Temperley, H.N.V.1
  • 88
    • 0035537476 scopus 로고    scopus 로고
    • Transfer matrices and partition-function zeros for antiferromagnetic potts models. II. Extended results for square-lattice chromatic polynomial
    • cond-mat/0011456, this issue
    • J. L. Jacobsen and J. Salas, Transfer matrices and partition-function zeros for antiferromagnetic Potts models. II. Extended results for square-lattice chromatic polynomial, cond-mat/0011456, J. Stat. Phys. 104:703 (2001), this issue.
    • (2001) J. Stat. Phys. , vol.104 , pp. 703
    • Jacobsen, J.L.1    Salas, J.2
  • 99
  • 100
    • 0003956966 scopus 로고
    • Wiley, Chichester
    • nd ed., vol. 2 (Wiley, Chichester, 1989).
    • (1989) nd Ed. , vol.2
    • Cohn, P.M.1
  • 101
    • 0003828291 scopus 로고
    • Chapman and Hall, London New York
    • nd ed. (Chapman and Hall, London New York, 1989).
    • (1989) nd Ed.
    • Stewart, I.1
  • 117
    • 0032489693 scopus 로고    scopus 로고
    • cond-mat/9711279
    • J. L. Jacobsen and J. Cardy, Nucl. Phys. B 515[FS]:701 (1998), cond-mat/9711279.
    • (1998) Nucl. Phys. B , vol.515 , Issue.FS , pp. 701
    • Jacobsen, J.L.1    Cardy, J.2
  • 119
    • 0003652674 scopus 로고    scopus 로고
    • Wadsworth & Brooks/Cole, Monterey, CA, Reprinted by Cambridge University Press
    • R. P. Stanley, Enumerative Combinatorics, vol. 1 (Wadsworth & Brooks/Cole, Monterey, CA, 1986). Reprinted by Cambridge University Press, 1999.
    • (1986) Enumerative Combinatorics , vol.1
    • Stanley, R.P.1
  • 120
    • 0003652674 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge-New York
    • R. P. Stanley, Enumerative Combinatorics, vol. 2 (Cambridge University Press, Cambridge-New York, 1999).
    • (1999) Enumerative Combinatorics , vol.2
    • Stanley, R.P.1
  • 123
  • 124
    • 0000278117 scopus 로고
    • R. L. Graham, M. Grötschel, and L. Lovász, eds. Elsevier/MIT Press, Amsterdam/Cambridge
    • A. M. Odlyzko, in Handbook of Combinatorics, vol. 2, R. L. Graham, M. Grötschel, and L. Lovász, eds. (Elsevier/MIT Press, Amsterdam/Cambridge, 1995), pp. 1063-1229.
    • (1995) Handbook of Combinatorics , vol.2 , pp. 1063-1229
    • Odlyzko, A.M.1
  • 132
    • 0003956970 scopus 로고
    • Addison-Wesley, Reading, Mass.
    • rd ed. (Addison-Wesley, Reading, Mass., 1993).
    • (1993) rd Ed.
    • Lang, S.1
  • 134
    • 0003734152 scopus 로고    scopus 로고
    • Software package available at http: //www.dm.unipi.it/pages/bini/public_html/software/mps2.tar.gz
    • D. A. Bini and G. Fiorentino, Numerical computation of polynomial roots: MPSolve-Version 2.0. FRISCO report (1998). Available at http://www. dm.unipi.it/pages /bini/public_html/papers/mpsolve.ps.Z. Software package available at http: //www.dm.unipi.it/pages/bini/public_html/software/mps2.tar.gz.
    • (1998) Numerical Computation of Polynomial Roots: MPSolve-Version 2.0. FRISCO Report
    • Bini, D.A.1    Fiorentino, G.2
  • 136
    • 0003862232 scopus 로고
    • corrected printing (Springer-Verlag, Berlin-New York)
    • nd ed., corrected printing (Springer-Verlag, Berlin-New York, 1980).
    • (1980) nd Ed.
    • Kato, T.1
  • 140
    • 0007166660 scopus 로고
    • Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, Western Michigan University, Y. Alavi et al., eds. Wiley, New York
    • R. C. Read and G. F. Royle, in Graph Theory, Combinatorics, and Applications (Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, Western Michigan University, 1988), Volume 2, Y. Alavi et al., eds. (Wiley, New York, 1991).
    • (1988) Graph Theory, Combinatorics, and Applications , vol.2
    • Read, R.C.1    Royle, G.F.2
  • 142
    • 0003904891 scopus 로고    scopus 로고
    • Springer-Verlag, New York-Berlin-Heidelberg
    • B. Bollobas, Modern Graph Theory (Springer-Verlag, New York-Berlin-Heidelberg, 1998).
    • (1998) Modern Graph Theory
    • Bollobas, B.1
  • 145
    • 0003455511 scopus 로고
    • Every planar map is four colorable
    • American Mathematical Society, Providence RI
    • K. Appel and W. Haken, Every Planar Map is Four Colorable, Contemporary Mathematics #98 (American Mathematical Society, Providence RI, 1989).
    • (1989) Contemporary Mathematics #98
    • Appel, K.1    Haken, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.