메뉴 건너뛰기




Volumn 100, Issue 5-6, 2000, Pages 893-904

Ising models on hyperbolic graphs II

Author keywords

Hyperbolic graphs; Ising models; Percolation

Indexed keywords


EID: 0034343872     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018763008810     Document Type: Article
Times cited : (34)

References (33)
  • 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. 8394
    • Aizenman, M.1
  • 4
    • 0002305414 scopus 로고    scopus 로고
    • Critical percolation on any non-amenable group has no infinite clusters
    • to appear
    • I. Benjamini, R. Lyons, Y. Peres, and O. Schramm, Critical percolation on any non-amenable group has no infinite clusters, Ann. Probab., to appear.
    • Ann. Probab.
    • Benjamini, I.1    Lyons, R.2    Peres, Y.3    Schramm, O.4
  • 8
    • 0000393829 scopus 로고
    • Density and uniqueness in percolation
    • R. M. Burton and M. Keane, Density and uniqueness in percolation, Commun. Math. Phys. 121:501-505 (1989).
    • (1989) Commun. Math. Phys. , vol.121 , pp. 501-505
    • Burton, R.M.1    Keane, M.2
  • 9
    • 0001722765 scopus 로고
    • Gibbs state describing coexistence of phases for a three-dimensional Ising model
    • R. L. Dobrushin, Gibbs state describing coexistence of phases for a three-dimensional Ising model, Theory Probab. Appl. 17:582 600 (1972).
    • (1972) Theory Probab. Appl. , vol.17 , pp. 582600
    • Dobrushin, R.L.1
  • 11
    • 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
  • 12
    • 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
  • 13
    • 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
  • 14
    • 21344436631 scopus 로고
    • The stochastic random-cluster process and the uniqueness of random-cluster measures
    • G. R. Grimmett, The stochastic random-cluster process and the uniqueness of random-cluster measures, Ann. Probab. 23:1461-1510 (1995).
    • (1995) Ann. Probab. , vol.23 , pp. 1461-1510
    • Grimmett, G.R.1
  • 15
    • 0000042426 scopus 로고
    • Percolation in cursive Greek chi + 1 dimensions
    • G. R. Grimmett and D. J. A. Welsh, eds. Clarendon Press, Oxford
    • G. R. Grimmett and C. M. Newman, Percolation in cursive Greek chi + 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
  • 17
    • 0038934720 scopus 로고    scopus 로고
    • Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously
    • O. Häggström and Y. Peres, Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously, Probab. Th. Rel. Fields 113:273-285 (1999).
    • (1999) Probab. Th. Rel. Fields , vol.113 , pp. 273-285
    • Häggström, O.1    Peres, Y.2
  • 18
    • 0001607313 scopus 로고
    • On the absence of non-translation invariant Gibbs states for the two dimensional Ising model
    • Esztergom, J. Fritz, J. L. Lebowitz and D. Szsz, eds. Amsterdam, North-Holland
    • Y. Higuchi, On the absence of non-translation invariant Gibbs states for the two dimensional Ising model, in Random Fields (Esztergom, 1979), J. Fritz, J. L. Lebowitz and D. Szsz, eds. (Amsterdam, North-Holland, 1981). Vol. I, pp. 517-534.
    • (1979) Random Fields , vol.1 , pp. 517-534
    • Higuchi, Y.1
  • 19
    • 0033070870 scopus 로고    scopus 로고
    • The random cluster model on a general graph and a phase transition characterization of nonamenability
    • J. Jonasson. The random cluster model on a general graph and a phase transition characterization of nonamenability, Stoch. Proc. Appl. 79:335-354 (1999).
    • (1999) Stoch. Proc. Appl. , vol.79 , pp. 335-354
    • Jonasson, J.1
  • 20
    • 85034179015 scopus 로고    scopus 로고
    • Amenability and phase transition in the Ising model
    • to appear
    • J. Jonasson and J. Steif, Amenability and phase transition in the Ising model, J. Theor. Probab., to appear.
    • J. Theor. Probab.
    • Jonasson, J.1    Steif, J.2
  • 22
    • 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
  • 23
    • 0000688715 scopus 로고
    • Random walks and the growth of groups
    • R. Lyons, Random walks and the growth of groups, C.R. Acad. Sci. Paris Sér. I Math. 320:1361-1366 (1995).
    • (1995) C.R. Acad. Sci. Paris Sér. I Math. , vol.320 , pp. 1361-1366
    • Lyons, R.1
  • 25
    • 85009909568 scopus 로고    scopus 로고
    • Indistinguishability of percolation clusters
    • to appear
    • R. Lyons and O. Schramm, Indistinguishability of percolation clusters, Ann. Probab., to appear.
    • Ann. Probab.
    • Lyons, R.1    Schramm, O.2
  • 26
    • 38249030408 scopus 로고
    • Isoperimetric inequalities, growth, and the spectrum of graphs
    • B. Mohar, Isoperimetric inequalities, growth, and the spectrum of graphs. Linear Algebra Appl. 103:119-131 (1988).
    • (1988) Linear Algebra Appl. , vol.103 , pp. 119-131
    • Mohar, B.1
  • 27
    • 0001227786 scopus 로고
    • Infinite clusters in percolation models
    • C. M. Newman and L. S. Schulman, Infinite clusters in percolation models, J. Stat. Phys. 26:613-628 (1981).
    • (1981) J. Stat. Phys. , vol.26 , pp. 613-628
    • Newman, C.M.1    Schulman, L.S.2
  • 28
    • 0000808037 scopus 로고
    • Markov fields on branching planes
    • C. M. Newman and C. C. Wu, Markov fields on branching planes, Probab. Th. Rel. Fields. 85:539-552 (1990).
    • (1990) Probab. Th. Rel. Fields. , vol.85 , pp. 539-552
    • Newman, C.M.1    Wu, C.C.2
  • 30
    • 0033077109 scopus 로고    scopus 로고
    • Stability of infinite clusters in supercritical percolation
    • R. H. Schonmann, Stability of infinite clusters in supercritical percolation, Probab. Th. Rel. Fields 113:287-300 (1999).
    • (1999) Probab. Th. Rel. Fields , vol.113 , pp. 287-300
    • Schonmann, R.H.1
  • 32
    • 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
  • 33
    • 0039862319 scopus 로고    scopus 로고
    • Ising models on hyperbolic graphs
    • C. C. Wu, Ising models on hyperbolic graphs, J. Stat. Phys. 85:251-259 (1997).
    • (1997) J. Stat. Phys. , vol.85 , pp. 251-259
    • Wu, C.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.