Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Necessary and sufficient conditions for the $\textrm {GHS}$ inequality with applications to analysis and probability
HTML articles powered by AMS MathViewer

by Richard S. Ellis and Charles M. Newman PDF
Trans. Amer. Math. Soc. 237 (1978), 83-99 Request permission


The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.
  • Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers, a division of John Wiley & Sons, Inc., New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043
  • Herm Jan Brascamp and Elliott H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Functional Analysis 22 (1976), no. 4, 366–389. MR 0450480, DOI 10.1016/0022-1236(76)90004-5
  • Paul R. Chernoff, Note on product formulas for operator semigroups, J. Functional Analysis 2 (1968), 238–242. MR 0231238, DOI 10.1016/0022-1236(68)90020-7
  • Richard S. Ellis, James L. Monroe, and Charles M. Newman, The GHS and other correlation inequalities for a class of even ferromagnets, Comm. Math. Phys. 46 (1976), no. 2, 167–182. MR 395659
  • Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
  • I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont., 1969. Translated from the Russian by Scripta Technica, Inc. MR 0247660
  • Robert B. Griffiths, Rigorous results for Ising ferromagnets of arbitrary spin, J. Mathematical Phys. 10 (1969), 1559–1565. MR 256682, DOI 10.1063/1.1665005
  • Robert B. Griffiths, C. A. Hurst, and S. Sherman, Concavity of magnetization of an Ising ferromagnet in a positive external field, J. Mathematical Phys. 11 (1970), 790–795. MR 266507, DOI 10.1063/1.1665211
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • Petr Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften, Band 151, Academia [Publishing House of the Czechoslovak Academy of Sciences], Prague; Springer-Verlag New York Inc., New York, 1968. MR 0247667
  • Barry Simon, Coupling constant analyticity for the anharmonic oscillator. (With appendix), Ann. Physics 58 (1970), 76–136. MR 416322, DOI 10.1016/0003-4916(70)90240-X
  • Barry Simon, The $P(\phi )_{2}$ Euclidean (quantum) field theory, Princeton Series in Physics, Princeton University Press, Princeton, N.J., 1974. MR 0489552
  • Barry Simon, Approximation of Feynman integrals and Markov fields by spin systems, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 399–402. MR 0441161
  • Garrett S. Sylvester, Representations and inequalities for Ising model Ursell functions, Comm. Math. Phys. 42 (1975), 209–220. MR 406301
  • Colin J. Thompson, Mathematical statistical mechanics, A Series of Books in Applied Mathematics, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1972. MR 0469020
  • E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
Similar Articles
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 237 (1978), 83-99
  • MSC: Primary 26A84; Secondary 35K99, 60J99, 82.60
  • DOI:
  • MathSciNet review: 0492131