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Volumn 125, Issue 3, 2003, Pages 305-349

Ornstein-Zernike theory for finite range Ising models above Tc

Author keywords

Ising model; Local limit theorems; Ornstein Zernike decay of correlations; Renormalization; Ruelle operator

Indexed keywords


EID: 0037933323     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-002-0229-z     Document Type: Article
Times cited : (74)

References (37)
  • 1
    • 0000876058 scopus 로고    scopus 로고
    • Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps
    • [AD]
    • [AD] Aaronson, J., Denker, M.: Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps, Stoch. Dyn. 1, 193-237 (2001)
    • (2001) Stoch. Dyn. , vol.1 , pp. 193-237
    • Aaronson, J.1    Denker, M.2
  • 2
    • 4243512919 scopus 로고
    • Ornstein-Zernike theory of classical fluids at low density
    • [AK]
    • [AK] Abraham, D.B., Kunz, H.: Ornstein-Zernike Theory of Classical Fluids at Low Density, Phys. Rev. Lett. 39, 1011 1014 (1977)
    • (1977) Phys. Rev. Lett. , vol.39 , pp. 1011-1014
    • Abraham, D.B.1    Kunz, H.2
  • 3
    • 33644572993 scopus 로고
    • 4 fields and Ising models. I, II
    • [Az]
    • 4 fields and Ising models. I, II, Comm. Math. Phys. 86, 1-48 (1982)
    • (1982) Comm. Math. Phys. , vol.86 , pp. 1-48
    • Aizenman, M.1
  • 4
    • 34250105066 scopus 로고
    • The phase transition in a general class oflsing-type models is sharp
    • [ABF]
    • [ABF] Aizenman, M., Barsky, D.J., Fernández, R.: The phase transition in a general class oflsing-type models is sharp, J. Stat. Phys. 47, 342-374 (1987)
    • (1987) J. Stat. Phys. , vol.47 , pp. 342-374
    • Aizenman, M.1    Barsky, D.J.2    Fernández, R.3
  • 6
    • 0031514908 scopus 로고    scopus 로고
    • Approximation of subadditive functions and convergence rates in limiting-shape results
    • [A1]
    • [A1] Alexander, K.S.: Approximation of subadditive functions and convergence rates in limiting-shape results. Ann. Prob. 25, 30-55 (1997)
    • (1997) Ann. Prob. , vol.25 , pp. 30-55
    • Alexander, K.S.1
  • 7
    • 85009367586 scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms
    • [Bow], Springer Berlin
    • [Bow] Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, LNM 470, Springer Berlin 1975
    • (1975) LNM , vol.470
    • Bowen, R.1
  • 8
    • 0033444391 scopus 로고    scopus 로고
    • Subshifts on an infinite alphabet
    • [Br]
    • [Br] Bressaud, X.: Subshifts on an infinite alphabet, Ergodic Theory Dynam. Systems 19, 1175-1200 (1999)
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , pp. 1175-1200
    • Bressaud, X.1
  • 9
    • 0001038009 scopus 로고
    • Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models
    • [BF]
    • [BF] Bricmont, J., Fröhlich, J.: Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models. Comm. Math. Phys. 98, 553-578 (1985)
    • (1985) Comm. Math. Phys. , vol.98 , pp. 553-578
    • Bricmont, J.1    Fröhlich, J.2
  • 10
    • 0009075651 scopus 로고
    • On the local structure of the phase separation line in the two-dimensional Ising system
    • [BLP]
    • [BLP] Bricmont, J., Lebowitz, J.L., Pfister, Ch.-E.: On the local structure of the phase separation line in the two-dimensional Ising svstem, J. Statist. Phys. 26, 313-332 (1981)
    • (1981) J. Statist. Phys. , vol.26 , pp. 313-332
    • Bricmont, J.1    Lebowitz, J.L.2    Pfister, Ch.-E.3
  • 11
    • 0000959608 scopus 로고
    • Gaussian fluctuations in the subcritical regime of percolation
    • [CCC]
    • [CCC] Campanino, M., Chayes, J.T., Chayes, L.: Gaussian fluctuations in the subcritical regime of percolation. Prob. Th. Rel. Fields, 88, 269-341 (1991)
    • (1991) Prob. Th. Rel. Fields , vol.88 , pp. 269-341
    • Campanino, M.1    Chayes, J.T.2    Chayes, L.3
  • 12
    • 0000440316 scopus 로고
    • Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures
    • [CC]
    • [CC] Chayes, J.T., Chayes, L.: Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures, Commun. Math. Phys. 105, 221 238 (1986)
    • (1986) Commun. Math. Phys. , vol.105 , pp. 221-238
    • Chayes, J.T.1    Chayes, L.2
  • 15
    • 21844525355 scopus 로고
    • Statistical properties of long return times in type I infermittency
    • [CIs]
    • [CIs] Campanino, M., Isola, S.: Statistical properties of long return times in type I infermittency, Forum Matem. 7, 331-348 (1995)
    • (1995) Forum Matem. , vol.7 , pp. 331-348
    • Campanino, M.1    Isola, S.2
  • 16
    • 0009128233 scopus 로고
    • Large and moderate deviations in the Ising model
    • [DS]
    • [DS] Dobrushin, R.L., Shlosman, S.: Large and moderate deviations in the Ising model, Advances Sov. Math., 20, 91-219 (1994)
    • (1994) Advances Sov. Math. , vol.20 , pp. 91-219
    • Dobrushin, R.L.1    Shlosman, S.2
  • 17
    • 33646656242 scopus 로고
    • Correlation functions and the critical region of simple fluids
    • [Fi]
    • [Fi] Fisher, M.: Correlation functions and the critical region of simple fluids, J. Mathematical Phys. 5, 944-962 (1964)
    • (1964) J. Mathematical Phys. , vol.5 , pp. 944-962
    • Fisher, M.1
  • 18
  • 19
    • 0009076781 scopus 로고
    • On some limit theorem related to the phase separation line in the two-dimensional Ising model
    • [Hi]
    • [Hi] Higuchi, Y.: On some limit theorem related to the phase separation line in the two-dimensional Ising model, Z. Wahrsch. Verw. Gebiete, 50, 287-315(1979)
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.50 , pp. 287-315
    • Higuchi, Y.1
  • 20
    • 0036103433 scopus 로고    scopus 로고
    • Surface tension and the Ornstein-Zemike behaviour for the 2D Blume-Capel model
    • [HK]
    • [HK] Hryniv, O., Kotecký, R.: Surface tension and the Ornstein-Zemike behaviour for the 2D Blume-Capel model, J. Stat. Phys. 106, 431-476 (2002)
    • (2002) J. Stat. Phys. , vol.106 , pp. 431-476
    • Hryniv, O.1    Kotecký, R.2
  • 21
    • 21344496131 scopus 로고
    • Large deviations for the 2D Ising model: A lower bound without cluster expansions
    • [Io1]
    • [Io1] Ioffe, D.: Large deviations for the 2D Ising model: a lower bound without cluster expansions, J. Stat. Phys. 74, 411-432 (1994)
    • (1994) J. Stat. Phys. , vol.74 , pp. 411-432
    • Ioffe, D.1
  • 26
    • 0030186902 scopus 로고    scopus 로고
    • Asymptotics of decay of correlation for lattice spin fields at high temperatures I. The Ising model
    • [MZ]
    • [MZ] Minlos, R.A., Zhizhina, H.A.: Asymptotics of decay of correlation for lattice spin fields at high temperatures I. The Ising model. J. Stat. Phys. 84, 85-118 (1996)
    • (1996) J. Stat. Phys. , vol.84 , pp. 85-118
    • Minlos, R.A.1    Zhizhina, H.A.2
  • 28
    • 84972570025 scopus 로고
    • The radius of the essential spectrum
    • [Nus 1]
    • [Nus 1] Nussbaum, R.D.: The radius of the essential spectrum. Duke. Math. J. 38, 473-478 (1970)
    • (1970) Duke. Math. J. , vol.38 , pp. 473-478
    • Nussbaum, R.D.1
  • 29
    • 0000984231 scopus 로고
    • Eigenvalues of nonlinear positive operators and the linear Krein-Rutman theorem, Fixed point theory
    • [Nus2], Springer
    • [Nus2] Nussbaum, R.D.: Eigenvalues of nonlinear positive operators and the linear Krein-Rutman theorem, Fixed point theory. LNM 886, 309-330, Springer (1980)
    • (1980) LNM , vol.886 , pp. 309-330
    • Nussbaum, R.D.1
  • 30
    • 0000981231 scopus 로고
    • Ornstein Zernike and analyticity properties of classical lattice spin systems
    • [P-L]
    • [P-L] Paes-Leme, P.J.: Ornstein Zernike and analyticity properties of classical lattice spin systems. Ann. Phys. (NY) 115, 367-387 (1978)
    • (1978) Ann. Phys. (NY) , vol.115 , pp. 367-387
    • Paes-Leme, P.J.1
  • 31
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structure of hyperbolic dynamics
    • [PP]
    • [PP] Parry, W., Pollicott, M.: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics. Astérisque 187-188 (1990)
    • (1990) Astérisque , pp. 187-188
    • Parry, W.1    Pollicott, M.2
  • 32
    • 0031505092 scopus 로고    scopus 로고
    • Large deviations and continuum limit in the 2D Ising model
    • [PV1]
    • [PV1] Pfister, C.-E., Velenik, Y.: Large deviations and continuum limit in the 2D Ising model. Prob. Th. Rel. Fields 109, 435-506 (1997)
    • (1997) Prob. Th. Rel. Fields , vol.109 , pp. 435-506
    • Pfister, C.-E.1    Velenik, Y.2
  • 33
    • 0033241779 scopus 로고    scopus 로고
    • Interface, surface tension and reentrant pinning tran-sition in the 2D Ising model
    • [PV2]
    • [PV2] Pfister, C.-F., Velenik, Y.: Interface, surface tension and reentrant pinning tran-sition in the 2D Ising model, Commun. Math. Phys. 204, 269-312 (1999)
    • (1999) Commun. Math. Phys. , vol.204 , pp. 269-312
    • Pfister, C.-F.1    Velenik, Y.2
  • 35
    • 0033276174 scopus 로고    scopus 로고
    • Thermodynamic formalism for countable Marker shifts
    • [Sa]
    • [Sa] Sarig, O.M.: Thermodynamic formalism for countable Marker shifts, Ergodic Theory Dynam. Systems 19, 1565-1593 (1999)
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , pp. 1565-1593
    • Sarig, O.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.