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Volumn 64, Issue 9, 2011, Pages 1165-1198

Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model

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EID: 79957682413     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20370     Document Type: Article
Times cited : (92)

References (29)
  • 1
    • 0001056718 scopus 로고    scopus 로고
    • Hölder regularity and dimension bounds for random curves
    • Aizenman, M.; Burchard, A. Hölder regularity and dimension bounds for random curves. Duke Math. J. 99 (1999), 419-453.
    • (1999) Duke Math. J , vol.99 , pp. 419-453
    • Aizenman, M.1    Burchard, A.2
  • 2
    • 79957768343 scopus 로고    scopus 로고
    • The critical temperature of the Ising model on the square lattice, an easy way. Preprint, arXiv:1010.0526
    • Beffara, V.; Duminil-Copin, H. The critical temperature of the Ising model on the square lattice, an easy way. Preprint, 2010. arXiv:1010.0526
    • (2010)
    • Beffara, V.1    Duminil-Copin, H.2
  • 3
    • 79957755739 scopus 로고    scopus 로고
    • The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1. Preprint, arXiv:1006.5073
    • Beffara, V.; Duminil-Copin, H. The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1. Preprint, 2010. arXiv:1006.5073
    • (2010)
    • Beffara, V.1    Duminil-Copin, H.2
  • 4
    • 0010882054 scopus 로고
    • Infinite conformal symmetry in twodimensional quantum field theory
    • Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B. Infinite conformal symmetry in twodimensional quantum field theory. Nucl. Phys. B 241 (1984), 333-380.
    • (1984) Nucl. Phys. B , vol.241 , pp. 333-380
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 5
    • 0004542587 scopus 로고
    • Infinite conformal symmetry of critical fluctuations in two dimensions
    • Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B. Infinite conformal symmetry of critical fluctuations in two dimensions. J. Stat. Phys. 34 (1984), 763-774.
    • (1984) J. Stat. Phys , vol.34 , pp. 763-774
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 6
    • 65249105535 scopus 로고    scopus 로고
    • Ising (conformal) fields and cluster area measures
    • Camia, F.; Newman, C. M. Ising (conformal) fields and cluster area measures. Proc. Natl. Acad. Sci. USA 106 (2009), 5457-5463.
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , pp. 5457-5463
    • Camia, F.1    Newman, C.M.2
  • 7
    • 84862730032 scopus 로고    scopus 로고
    • Universality in the 2D Ising model and conformal invariance of fermionic observables
    • in press.
    • Chelkak, D.; Smirnov, S. Universality in the 2D Ising model and conformal invariance of fermionic observables. Invent. Math., in press.
    • Invent. Math.
    • Chelkak, D.1    Smirnov, S.2
  • 8
    • 0001440863 scopus 로고
    • Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm
    • Edwards, R. G.; Sokal, A. D. Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D 38 (1988), 2009-2012.
    • (1988) Phys. Rev. D , vol.38 , pp. 2009-2012
    • Edwards, R.G.1    Sokal, A.D.2
  • 9
    • 0041855748 scopus 로고
    • On the random-cluster model. I. Introduction and relation to other models
    • Fortuin, C. M.; Kasteleyn, P. W. On the random-cluster model. I. Introduction and relation to other models. Physica 57 (1972), 536-564.
    • (1972) Physica , vol.57 , pp. 536-564
    • Fortuin, C.M.1    Kasteleyn, P.W.2
  • 12
    • 79957711119 scopus 로고    scopus 로고
    • On random planar curves and their scaling limits. Doctoral dissertation, University of Helsinki
    • Kemppainen, A. On random planar curves and their scaling limits. Doctoral dissertation, University of Helsinki, 2009.
    • (2009)
    • Kemppainen, A.1
  • 13
    • 79957756996 scopus 로고    scopus 로고
    • Random curves, scaling limits and Loewner evolutions. In preparation.
    • Kemppainen, A.; Smirnov, S. Random curves, scaling limits and Loewner evolutions. In preparation.
    • Kemppainen, A.1    Smirnov, S.2
  • 14
    • 0001755621 scopus 로고
    • Scaling relations for 2D-percolation
    • Kesten, H. Scaling relations for 2D-percolation. Comm. Math. Phys. 109 (1987), 109-156.
    • (1987) Comm. Math. Phys , vol.109 , pp. 109-156
    • Kesten, H.1
  • 16
    • 0242384526 scopus 로고    scopus 로고
    • One-arm exponent for critical 2D percolation
    • Lawler, G. F.; Schramm, O.; Werner, W. One-arm exponent for critical 2D percolation. Elec. J. Probab. 7 (2002), 1-13.
    • (2002) Elec. J. Probab , vol.7 , pp. 1-13
    • Lawler, G.F.1    Schramm, O.2    Werner, W.3
  • 17
    • 79957698041 scopus 로고    scopus 로고
    • Critical Ising on the square lattice mixes in polynomial time. Preprint, arXiv:1001.1613
    • Lubetzky, E.; Sly, A. Critical Ising on the square lattice mixes in polynomial time. Preprint, 2010. arXiv:1001.1613
    • (2010)
    • Lubetzky, E.1    Sly, A.2
  • 18
    • 36149012281 scopus 로고
    • Crystal statistics. I. A two-dimensional model with an order-disorder transition
    • Onsager, L. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2) 65 (1944), 117-149.
    • (1944) Phys. Rev. (2) , vol.65 , pp. 117-149
    • Onsager, L.1
  • 19
    • 84924799755 scopus 로고
    • On Ising's model of ferromagnetism
    • Peierls, R. On Ising's model of ferromagnetism. Math. Proc. Camb. Phil. Soc. 32 (1936), 477-481.
    • (1936) Math. Proc. Camb. Phil. Soc , vol.32 , pp. 477-481
    • Peierls, R.1
  • 20
    • 0014928682 scopus 로고
    • Conformal symmetry of critical fluctuations
    • Polyakov, A. M. Conformal symmetry of critical fluctuations. JETP Letters 12 (1970), 381-383.
    • (1970) JETP Letters , vol.12 , pp. 381-383
    • Polyakov, A.M.1
  • 22
    • 77957093986 scopus 로고
    • Percolation probabilities on the square lattice
    • Seymour, P. D.; Welsh, D. J. A. Percolation probabilities on the square lattice. Ann. Discrete Math. 3 (1978), 227-245.
    • (1978) Ann. Discrete Math , vol.3 , pp. 227-245
    • Seymour, P.D.1    Welsh, D.J.A.2
  • 23
    • 84878094646 scopus 로고    scopus 로고
    • Towards conformal invariance of 2D lattice models
    • Smirnov, S. Towards conformal invariance of 2D lattice models. Proc. ICM 2006 vol. 2 (2007), 1421-1451.
    • (2007) Proc. ICM 2006 , vol.2 , pp. 1421-1451
    • Smirnov, S.1
  • 24
    • 77957693837 scopus 로고    scopus 로고
    • Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
    • Smirnov, S. Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model. Ann. Math. 172-2 (2010), 1435-1467.
    • (2010) Ann. Math , vol.172 , Issue.2 , pp. 1435-1467
    • Smirnov, S.1
  • 25
    • 79957761266 scopus 로고    scopus 로고
    • Conformal invariance in random cluster models. II. Scaling limit of the interface. In preparation.
    • Smirnov, S. Conformal invariance in random cluster models. II. Scaling limit of the interface. In preparation.
    • Smirnov, S.1
  • 26
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • Smirnov, S.; Werner, W. Critical exponents for two-dimensional percolation. Math. Res. Lett. 8 (2001), 729-744.
    • (2001) Math. Res. Lett , vol.8 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 28
    • 0242330847 scopus 로고    scopus 로고
    • SLEs as boundaries of clusters of Brownian loops
    • Werner, W. SLEs as boundaries of clusters of Brownian loops. C. R. Math. Acad. Sci. Paris 337 (2003), 481-486.
    • (2003) C. R. Math. Acad. Sci. Paris , vol.337 , pp. 481-486
    • Werner, W.1
  • 29
    • 79957732420 scopus 로고    scopus 로고
    • Percolation et modèle d'Ising. Cours Spécialisés de la SMF 16
    • Werner, W. Percolation et modèle d'Ising. Cours Spécialisés de la SMF 16, 2010.
    • (2010)
    • Werner, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.