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Volumn 97, Issue 1-2, 1999, Pages 67-86

The Swendsen-Wang process does not always mix rapidly

Author keywords

Ferromagnetic Potts model; First order phase transition; Mixing time; Random graph model; Swendsen Wang dynamics

Indexed keywords


EID: 0033211906     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004610900745     Document Type: Article
Times cited : (66)

References (31)
  • 1
    • 0001051761 scopus 로고
    • On the computational complexity of Ising spin glass models
    • F. Barahona, On the computational complexity of Ising spin glass models, J. Phys. A: Math. Gen. 15:3241-3253 (1982).
    • (1982) J. Phys. A: Math. Gen. , vol.15 , pp. 3241-3253
    • Barahona, F.1
  • 8
    • 0001440863 scopus 로고
    • Generalizations of the Fortuin-Kasteleyn Swendsen Wang representation and Monte Carlo algorithm
    • R. G. Edwards and A. D. Sokal, Generalizations of the Fortuin-Kasteleyn Swendsen Wang representation and Monte Carlo algorithm. Phys. Rev. D 38:2009-2012 (1988).
    • (1988) Phys. Rev. D , vol.38 , pp. 2009-2012
    • Edwards, R.G.1    Sokal, A.D.2
  • 9
    • 0003207906 scopus 로고
    • Entropy, large deviations, and statistical mechanics
    • Springer-Verlag
    • R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics, Grundlehren der mathematischen Wissenschaften, Vol. 271 (Springer-Verlag, 1985).
    • (1985) Grundlehren der Mathematischen Wissenschaften , vol.271
    • Ellis, R.S.1
  • 10
    • 0041855748 scopus 로고
    • On the random cluster model I: Introduction and relation to other models
    • C. M. Fortuin and P. W. Kasteleyn, On the random cluster model I: Introduction and relation to other models, Physica 57:536-564 (1972).
    • (1972) Physica , vol.57 , pp. 536-564
    • Fortuin, C.M.1    Kasteleyn, P.W.2
  • 12
    • 0027677367 scopus 로고
    • Polynomial-time approximation algorithms for the Ising model
    • M. Jerrum and A. Sinclair, Polynomial-time approximation algorithms for the Ising model, SIAM J. Comput. 22:1087-1116 (1993).
    • (1993) SIAM J. Comput. , vol.22 , pp. 1087-1116
    • Jerrum, M.1    Sinclair, A.2
  • 13
    • 84990721683 scopus 로고
    • A very simple algorithm for estimating the number of k-colourings of a low-degree graph
    • M. Jerrum, A very simple algorithm for estimating the number of k-colourings of a low-degree graph, Random Structures and Algorithms 7:157-165 (1995).
    • (1995) Random Structures and Algorithms , vol.7 , pp. 157-165
    • Jerrum, M.1
  • 14
    • 0002734223 scopus 로고    scopus 로고
    • The Markov chain Monte Carlo method: An approach to approximate counting and integration
    • Dorit Hochbaum, ed. PWS
    • M. Jerrum and A. Sinclair, The Markov chain Monte Carlo method: An approach to approximate counting and integration. In Approximation Algorithms for NP-hard Problems, Dorit Hochbaum, ed. (PWS, 1996), pp. 482-520.
    • (1996) Approximation Algorithms for NP-hard Problems , pp. 482-520
    • Jerrum, M.1    Sinclair, A.2
  • 17
    • 84990713780 scopus 로고
    • The transitive closure of a random digraph
    • R. M. Karp, The transitive closure of a random digraph, Random Structures and Algorithms 1:73-93 (1990).
    • (1990) Random Structures and Algorithms , vol.1 , pp. 73-93
    • Karp, R.M.1
  • 18
    • 0003182706 scopus 로고
    • Behavior in large dimensions of the Potts and Heisenberg models
    • H. Kesten and R. H. Schonmann, Behavior in large dimensions of the Potts and Heisenberg models, Rev. Math. Phys. 1:147-182 (1990).
    • (1990) Rev. Math. Phys. , vol.1 , pp. 147-182
    • Kesten, H.1    Schonmann, R.H.2
  • 19
    • 0001964461 scopus 로고
    • Interfaces in the Potts model I: Piragov-Sinai theory of the Fortuin-Kasteleyn representation
    • L. Laanait, A. Messager, S. Miracle-Sole, J. Ruiz, and S. Shlosman, Interfaces in the Potts model I: Piragov-Sinai theory of the Fortuin-Kasteleyn representation. Commun. Math. Phys. 140:81-91 (1991).
    • (1991) Commun. Math. Phys. , vol.140 , pp. 81-91
    • Laanait, L.1    Messager, A.2    Miracle-Sole, S.3    Ruiz, J.4    Shlosman, S.5
  • 20
    • 0001035413 scopus 로고
    • On the method of bounded differences
    • Cambridge University Press
    • C. McDiarmid, On the method of bounded differences, London Mathematical Society Lecture Note Series, Vol. 141 (Cambridge University Press, 1989), pp. 148-188.
    • (1989) London Mathematical Society Lecture Note Series , vol.141 , pp. 148-188
    • McDiarmid, C.1
  • 24
    • 0032023977 scopus 로고    scopus 로고
    • Some large deviation results for sparse random graphs
    • Neil O'Connell, Some large deviation results for sparse random graphs, Prob. Theo. Rel. Fields 10:277-285 (1998).
    • (1998) Prob. Theo. Rel. Fields , vol.10 , pp. 277-285
    • O'Connell, N.1
  • 25
    • 84926736518 scopus 로고
    • Some generalised order-disorder transformations
    • R. B. Potts, Some generalised order-disorder transformations, Proc. Cambridge Phil. Soc. 48:106-109 (1952).
    • (1952) Proc. Cambridge Phil. Soc. , vol.48 , pp. 106-109
    • Potts, R.B.1
  • 26
    • 0038967484 scopus 로고    scopus 로고
    • Absence of phase transition for antiferromagnetic Potts models via the dobrushin uniqueness theorem
    • J. Salas and A. D. Sokal, Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem, J. Stat. Phys. 86:551-579 (1997).
    • (1997) J. Stat. Phys. , vol.86 , pp. 551-579
    • Salas, J.1    Sokal, A.D.2
  • 27
    • 84971804758 scopus 로고
    • Improved bounds for mixing rates of Markov chains and multicommodity flows
    • Alistair Sinclair, Improved bounds for mixing rates of Markov chains and multicommodity flows, Combin. Prob. Comput. 1:351-370 (1992).
    • (1992) Combin. Prob. Comput. , vol.1 , pp. 351-370
    • Sinclair, A.1
  • 28
    • 0009146617 scopus 로고
    • Personal communication
    • A. Sokal, Personal communication (1995).
    • (1995)
    • Sokal, A.1
  • 29
    • 33747349191 scopus 로고
    • Non-universal critical dynamics in Monte-Carlo simulations
    • R. H. Swendsen and J.-S. Wang, Non-universal critical dynamics in Monte-Carlo simulations, Phys. Rev. Lett. 58:86-88 (1987).
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 86-88
    • Swendsen, R.H.1    Wang, J.-S.2
  • 30
    • 0002072110 scopus 로고
    • The computational complexity of some classical problems from statistical physics
    • Oxford University Press
    • D. J. A. Welsh, The computational complexity of some classical problems from statistical physics, In Disorder in Physical Systems (Oxford University Press, 1990), pp. 307-321.
    • (1990) Disorder in Physical Systems , pp. 307-321
    • Welsh, D.J.A.1
  • 31
    • 0003238314 scopus 로고
    • Complexity: Knots, colourings and counting
    • Cambridge University Press
    • D. J. A. Welsh, Complexity: Knots, colourings and counting, London Mathematical Society Lecture Notes, Vol. 186 (Cambridge University Press, 1993).
    • (1993) London Mathematical Society Lecture Notes , vol.186
    • Welsh, D.J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.