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Volumn 85, Issue 1-2, 1996, Pages 251-259

Ising models on hyperbolic graphs

Author keywords

Fortuin Kasteleyn random cluster models; Hyperbolic graphs; Ising Potts models

Indexed keywords


EID: 0039862319     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02175564     Document Type: Article
Times cited : (36)

References (19)
  • 1
    • 0002014946 scopus 로고
    • Translation invariance and instability of phase coexistence in the two dimensional Ising system
    • M. Aizenman,Translation invariance and instability of phase coexistence in the two dimensional Ising system. Commun. Math. Phys. 73:83-94 (1980).
    • (1980) Commun. Math. Phys. , vol.73 , pp. 83-94
    • Aizenman, M.1
  • 3
    • 0001707493 scopus 로고
    • Strict monotonicity for critical points in percolation and ferromagnetic models
    • M. Aizenman and G. R. Grimmett, Strict monotonicity for critical points in percolation and ferromagnetic models, J. Stat. Phys. 63:817-835 (1991).
    • (1991) J. Stat. Phys. , vol.63 , pp. 817-835
    • Aizenman, M.1    Grimmett, G.R.2
  • 6
    • 0003165628 scopus 로고
    • Existence of a phase transition in two and three dimensional ising models
    • R. L. Dobrushin, Existence of a phase transition in two and three dimensional Ising models, Theory Prob. Appl. 10:193-213 (1965).
    • (1965) Theory Prob. Appl. , vol.10 , pp. 193-213
    • Dobrushin, R.L.1
  • 7
    • 33749860660 scopus 로고
    • On the random cluster model. III. The simple random cluster model
    • C. M. Fortuin, On the random cluster model. III. The simple random cluster model, Physica 59:545-570 (1972).
    • (1972) Physica , vol.59 , pp. 545-570
    • Fortuin, C.M.1
  • 8
    • 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
  • 9
    • 0002160945 scopus 로고
    • Equilibrium states of the ising model in the two phase region
    • G. Gallavotti and S. Miracle-Sole, Equilibrium states of the Ising model in the two phase region, Phys. Rev. B 5:2555-2559 (1972).
    • (1972) Phys. Rev. B , vol.5 , pp. 2555-2559
    • Gallavotti, G.1    Miracle-Sole, S.2
  • 10
    • 0000125498 scopus 로고
    • Peierls' proof of spontaneous magnetization in a two-dimensional Ising ferromagnet
    • R. B. Griffiths, Peierls' proof of spontaneous magnetization in a two-dimensional Ising ferromagnet, Phys. Rev. 136A-437-439 (1964).
    • (1964) Phys. Rev. , vol.136 A , pp. 437-439
    • Griffiths, R.B.1
  • 12
    • 0000042426 scopus 로고
    • Percolation in ∝ + 1 dimensions
    • G. R. Grimmett and D. J. A. Welsh, eds. Clarendon Press, Oxford
    • G. R. Grimmett and C. M. Newman, Percolation in ∝ + 1 dimensions, in Disorder in Physical Systems, G. R. Grimmett and D. J. A. Welsh, eds. (Clarendon Press, Oxford, 1990), pp. 167-190.
    • (1990) Disorder in Physical Systems , pp. 167-190
    • Grimmett, G.R.1    Newman, C.M.2
  • 13
    • 0001607313 scopus 로고
    • On the absence of non-translation invariant Gibbs states for the two dimensional Ising model
    • J. Fritz, J. L. Lebowitz, and D. Szsz, eds. North-Holland, Amsterdam
    • Y. Higuchi, On the absence of non-translation invariant Gibbs states for the two dimensional Ising model, in Random Fields, J. Fritz, J. L. Lebowitz, and D. Szsz, eds. (North-Holland, Amsterdam, 1981), Vol. I, pp. 517-534.
    • (1981) Random Fields , vol.1 , pp. 517-534
    • Higuchi, Y.1
  • 14
    • 0001446038 scopus 로고
    • Coexistence of phases in Ising ferromagnets
    • J. L. Lebowitz, Coexistence of phases in Ising ferromagnets, J. Stat. Phys. 16:463-476 (1977).
    • (1977) J. Stat. Phys. , vol.16 , pp. 463-476
    • Lebowitz, J.L.1
  • 16
    • 0000117732 scopus 로고
    • Equilibrium states of the two-dimensional Ising model in the two-phase region
    • A. Messager and S. Miracle-Sole, Equilibrium states of the two-dimensional Ising model in the two-phase region, Commun. Math. Phys. 40:187-196 (1975).
    • (1975) Commun. Math. Phys. , vol.40 , pp. 187-196
    • Messager, A.1    Miracle-Sole, S.2
  • 18
    • 84924799755 scopus 로고
    • On Ising's model of ferromagnetism
    • R. Peierls, On Ising's model of ferromagnetism, Proc. Camb. Philos. Soc. 32:477-481 (1936).
    • (1936) Proc. Camb. Philos. Soc. , vol.32 , pp. 477-481
    • Peierls, R.1
  • 19
    • 0002500545 scopus 로고
    • Ising models on the Lobachevsky plane
    • C. M. Series and Y. G. Sinai, Ising models on the Lobachevsky plane, Commun. Math. Phys. 128:63-76 (1990).
    • (1990) Commun. Math. Phys. , vol.128 , pp. 63-76
    • Series, C.M.1    Sinai, Y.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.