DOI: 10.1007/bf01007515. The phase transition in a general class of Ising-type models is sharp

The phase transition in a general class of Ising-type models is sharp

10.1007/bf01007515

Crossref journal-article

Springer Science and Business Media LLC

Journal of Statistical Physics (297)

Bibliography

Aizenman, M., Barsky, D. J., & Fernï¿½ndez, R. (1987). The phase transition in a general class of Ising-type models is sharp. Journal of Statistical Physics, 47(3â4), 343â374.

Authors 3

M. Aizenman (first)
D. J. Barsky (additional)
R. Fern�ndez (additional)

References 24 Referenced 102

M. Aizenman, Rigorous studies of critical behavior. II, inStatistical Physics and Dynamical Systems: Rigorous Results, J. Fritz, A. Jaffe, and D. Sz�sz, eds. (Birkh�user, Boston, 1985); Absence of an intermediate phase for a general class of one-component ferromagnetic models,Phys. Rev. Lett. 54: 839?842 (1985). / Statistical Physics and Dynamical Systems: Rigorous Results by M. Aizenman (1985)
M. Aizenman and D. J. Barsky, Sharpness of the phase transition in percolation models,Commun. Math. Phys. 108:489?526 (1987). (10.1007/BF01212322) / Commun. Math. Phys. by M. Aizenman (1987)
M. Aizenman and R. Graham, On the renormalized coupling constant and the susceptibility in ? 4 4 field theory and the Ising model in four dimensions,Nucl. Phys. B 225[FS9]:261?288 (1983). (10.1016/0550-3213(83)90053-6) / Nucl. Phys. B by M. Aizenman (1983)
J. Fr�hlich and A. D. Sokal, The random walk representation of classical spin systems and correlation inequalities. III. Nonzero magnetic field, in preparation.
J. T. Chayes and L. Chayes, An inequality for the infinite cluster density in Bernoulli percolation,Phys. Rev. Lett. 56:1619?1622 (1986). (10.1103/PhysRevLett.56.1619) / Phys. Rev. Lett. by J. T. Chayes (1986)
R. B. Griffiths, Rigorous results for Ising ferromagnets of arbitrary spin,J. Math. Phys. 10:1559?1565 (1969). (10.1063/1.1665005) / J. Math. Phys. by R. B. Griffiths (1969)
B. Simon and R. B. Griffiths, The (?4)2 field theory as a classical Ising model,Commun. Math. Phys. 33:145?164 (1973). (10.1007/BF01645626) / Commun. Math. Phys. by B. Simon (1973)
T. D. Lee and C. N. Yang, Statistical theory of equations of state and phase transitions, II, Lattice gas and Ising model,Phys. Rev. 87:410?419 (1952). (10.1103/PhysRev.87.410) / Phys. Rev. by T. D. Lee (1952)
R. Peierls, On Ising's model of ferromagnetism,Proc. Camb. Phil. Soc. 32:477?481 (1936); see also R. B. Griffiths, Peierls proof of spontaneous magnetization in a two-dimensional Ising ferromagnet,Phys. Rev. 136A:437?439 (1964); R. L. Dobrushin, The existence of a phase transition in the two- and three-dimensional Ising models,Teorija Verojatn. Prim. 10:209?230 (1965). (10.1017/S0305004100019174) / Proc. Camb. Phil. Soc. by R. Peierls (1936)
P. J. Thouless, Long range order in one-dimensional Ising systems,Phys. Rev. 187:732?733 (1969); see also F. Dyson, Existence of a phase transition in a one-dimensional Ising ferromagnet,Commun. Math. Phys. 12:91?107 (1969); P. W. Anderson, G. Yuvall, and D. R. Hamaan, Exact results in the Kondo problem. II. Scaling theory, qualitatively correct solution and some new results on one-dimensional classical statistical models,Phys. Rev. B 1:4464?4473 (1970). (10.1103/PhysRev.187.732) / Phys. Rev. by P. J. Thouless (1969)
J. Fr�hlich and T. Spencer, The phase transition in the one-dimensional Ising model with the 1/r 2 interaction energy,Commun. Math. Phys. 84:87?101 (1982); see also M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman: Discontinuity of the order parameter in one dimensional 1/�x?y�2 Ising and Potts models, to be submitted for publication. (10.1007/BF01208373) / Commun. Math. Phys. by J. Fr�hlich (1982)
J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems,J. Phys.C 6:1181?1203 (1973); see also S. Elitzur, R. Pearson, and J. Shigemitsu, Phase structure of discrete Abelian spin and gauge systems,Phys. Rev. D 19:3698?3714 (1979). (10.1088/0022-3719/6/7/010) / J. Phys.C by J. M. Kosterlitz (1973)
J. Fr�hlich and T. Spencer, The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas,Commun. Math. Phys. 81:527?602 (1981). (10.1007/BF01208273) / Commun. Math. Phys. by J. Fr�hlich (1981)
B. Simon, Correlation inequalities and the decay of correlations in ferromagnets,Commun. Math. Phys. 77:111?126 (1980). (10.1007/BF01982711) / Commun. Math. Phys. by B. Simon (1980)
J. L. Lebowitz, Coexistence of phases in Ising ferromagnets,J. Stat. Phys. 16:463?476 (1977). (10.1007/BF01152284) / J. Stat. Phys. by J. L. Lebowitz (1977)
M. Aizenman and R. Fern�ndez, On the critical behavior of the magnetization in highdimensional Ising models,J. Stat. Phys. 44:393?454 (1986). (10.1007/BF01011304) / J. Stat. Phys. by M. Aizenman (1986)
K. G. Wilson and M. E. Fisher, Critical exponents in 3.99 dimensions,Phys. Rev. Lett. 28:240?243 (1970). (10.1103/PhysRevLett.28.240) / Phys. Rev. Lett. by K. G. Wilson (1970)
A. B. Harris, T. C. Lubensky, W. K. Holcomb, and C. Dasgupta, Renormalization group approach to percolation problems,Phys. Rev. Lett. 35:327?330 (1975). (10.1103/PhysRevLett.35.327) / Phys. Rev. Lett. by A. B. Harris (1975)
M. Aizenman, Geometric analysis of ? 4 2 fields and Ising models. Parts I and II,Commun. Math. Phys. 86:1?48 (1982). (10.1007/BF01205659) / Commun. Math. Phys. by M. Aizenman (1982)
M. Aizenman and C. M. Newman, Tree graph inequalities and critical behavior in percolation models,J. Stat. Phys. 36:107?143 (1984). (10.1007/BF01015729) / J. Stat. Phys. by M. Aizenman (1984)
R. B. Griffiths, C. A. Hurst, and S. Sherman, Concavity of the magnetization of an Ising ferromagnet in a positive external field,J. Math. Phys. 11:790?795 (1970). (10.1063/1.1665211) / J. Math. Phys. by R. B. Griffiths (1970)
M. Aizenman, Rigorous studies of critical behavior, inApplications of Field Theory in Statistical Mechanics, L. Garrido, ed. (Springer-Verlag, Lecture Notes in Physics, 1985).
R. B. Griffiths, Correlations in Ising ferromagnets. II. External magnetic fields,J. Math. Phys. 8:484?489 (1967). (10.1063/1.1705220) / J. Math. Phys. by R. B. Griffiths (1967)
D. C. Brydges, J. Fr�hlich, and T. Spencer, The random walk representation of classical spin systems and correlation inequalities,Commun. Math. Phys. 83:123?150 (1982); see also J. Fr�hlich, On the triviality of ?? d 4 theories and the approach to the critical point ind ? > 4 dimensions,Nucl. Phys. B 200[FS4]:281?296 (1982); D. Brydges, J. Fr�hlich, and A. D. Sokal, The random walk representation of classical spin systems and correlation inequalities. II. The skeleton inequalities,Commun. Math. Phys. 91:117?139 (1983). (10.1007/BF01947075) / Commun. Math. Phys. by D. C. Brydges (1982)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 19, 2005, 3:33 a.m.)
Deposited	6 years, 4 months ago (April 26, 2019, 8:04 p.m.)
Indexed	1 month ago (July 30, 2025, 9:58 a.m.)
Issued	38 years, 4 months ago (May 1, 1987)
Published	38 years, 4 months ago (May 1, 1987)
Published Print	38 years, 4 months ago (May 1, 1987)

Funders 0

None

BibTeX

@article{Aizenman_1987, title={The phase transition in a general class of Ising-type models is sharp}, volume={47}, ISSN={1572-9613}, url={http://dx.doi.org/10.1007/bf01007515}, DOI={10.1007/bf01007515}, number={3–4}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Aizenman, M. and Barsky, D. J. and Fern�ndez, R.}, year={1987}, month=may, pages={343–374} }

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