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Volumn 55, Issue 5, 1997, Pages 5165-5178

Asymptotic limits and zeros of chromatic polynomials and ground-state entropy of Potts antiferromagnets

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EID: 0000931941     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.5165     Document Type: Article
Times cited : (100)

References (61)
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    • W. T. Tutte, Graph Theory, Vol. 21 of Encyclopedia of Mathematics and Its Applications, edited by G. C. Rota (Addison-Wesley, New York, 1984)
    • W. T. Tutte, Graph Theory, Vol. 21 of Encyclopedia of Mathematics and Its Applications, edited by G. C. Rota (Addison-Wesley, New York, 1984).
  • 10
    • 85037207251 scopus 로고    scopus 로고
    • As is well known, boundary conditions do not affect the thermodynamic limit except in the sense that they can affect which of the degenerate ground states the system picks in the broken-symmetry phase
    • As is well known, boundary conditions do not affect the thermodynamic limit except in the sense that they can affect which of the degenerate ground states the system picks in the broken-symmetry phase.
  • 20
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    • F.-M. Dong and Y. Liu, Discrete Math. 145, 95 (1995).
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    • Liu, Y.1
  • 24
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    • Communications with I. Enting and G. Baker are acknowledged
    • Their function denoted (Formula presented)(hc, q) is implicitly defined per 2-cell rather than per site and hence is the square of the function denoted (Formula presented)(hc, q) here, in Ref. 30, and in G. A. Baker, Jr., ., J. Combin. Theory 10, 217 (1971). Communications with I. Enting and G. Baker are acknowledged.
    • (1971) J. Combin. Theory , vol.10 , pp. 217
    • Baker, G.A.1
  • 33
    • 85037254208 scopus 로고    scopus 로고
    • This boundary itself has a complex-temperature extension that can be probed via calculations of zeros of the Potts partition function
    • This boundary itself has a complex-temperature extension that can be probed via calculations of zeros of the Potts partition function;
  • 35
    • 0002493774 scopus 로고    scopus 로고
    • Phys. Rev. Lett.ibid. 76, 173 (1996);
    • (1996) , vol.76 , pp. 173
    • Wu, F.Y.1
  • 36
    • 0001388893 scopus 로고    scopus 로고
    • for earlier work see P. P. Martin, Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991)
    • V. Matveev and R. Shrock, Phys. Rev. E 54, 6174 (1996); for earlier work see P. P. Martin, Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991).
    • (1996) Phys. Rev. E , vol.54 , pp. 6174
    • Matveev, V.1    Shrock, R.2
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    • Shrock, R.1
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    • Ground-state entropy without frustration can also occur in models with continuous variables and interactions
    • Ground-state entropy without frustration can also occur in models with continuous variables and interactions;
  • 53
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    • C. Y. Pan and X. Chen, Int. J. Mod. Phys. Bibid. 2, 1503 (1988).
    • (1988) , vol.2 , pp. 1503
    • Pan, C.Y.1    Chen, X.2
  • 58
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    • We note that the lower bound for W(sq, q) from this work coincides with the d=2 special case of an estimated lower bound applicable to d-dimensional Cartesian lattices (Formula presented), viz., W((Formula presented), q)⩾1+(q-2(Formula presented)/(q-1(Formula presented), presented by D. C. Mattis, Int. J. Mod. Phys. B 1, 103 (1987);
    • (1987) Int. J. Mod. Phys. B , vol.1 , pp. 103
    • Mattis, D.C.1
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    • K. Dohmen, J. Graph. Theoryibid. 17, 75 (1993).
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.