Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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.


Is our mathematics natural? The case of equilibrium statistical mechanics
HTML articles powered by AMS MathViewer

by David Ruelle PDF
Bull. Amer. Math. Soc. 19 (1988), 259-268
    1. P. Cartier, La pratique—et les pratiques—des mathématiques, Encyclopédie Philosophique Universelle, Presses Univ. de France, Paris, 1988 (to appear).
  • Eugene P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences [Comm. Pure Appl. Math. 13 (1960), 1–14; Zbl 102, 7], Mathematical analysis of physical systems, Van Nostrand Reinhold, New York, 1985, pp. 1–14. MR 824292
  • David Ruelle, Statistical mechanics: Rigorous results, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0289084
  • Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. MR 0442989, DOI 10.1007/BFb0081279
  • David Ruelle, Thermodynamic formalism, Encyclopedia of Mathematics and its Applications, vol. 5, Addison-Wesley Publishing Co., Reading, Mass., 1978. The mathematical structures of classical equilibrium statistical mechanics; With a foreword by Giovanni Gallavotti and Gian-Carlo Rota. MR 511655
  • Robert B. Israel, Convexity in the theory of lattice gases, Princeton Series in Physics, Princeton University Press, Princeton, N.J., 1979. With an introduction by Arthur S. Wightman. MR 517873
  • Ya. G. Sinaĭ, Theory of phase transitions: rigorous results, International Series in Natural Philosophy, vol. 108, Pergamon Press, Oxford-Elmsford, N.Y., 1982. Translated from the Russian by J. Fritz, A. Krámli, P. Major and D. Szász. MR 691854
  • D. Ruelle, Correlation functionals, J. Mathematical Phys. 6 (1965), 201–220. MR 201174, DOI 10.1063/1.1704272
  • 9. O. E. Lanford, Entropy and equilibrium states in classical statistical mechanics, Statistical Mechanics and Mathematical Problems, Lecture Notes in Physics, vol. 20, Springer-Verlag, Berlin, 1973, pp. 1-113.
  • T. D. Lee and C. N. Yang, Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model, Phys. Rev. (2) 87 (1952), 410–419. MR 53029, DOI 10.1103/PhysRev.87.410
  • Ja. G. Sinaĭ, Markov partitions and U-diffeomorphisms, Funkcional. Anal. i Priložen 2 (1968), no. 1, 64–89 (Russian). MR 0233038
  • Ja. G. Sinaĭ, Construction of Markov partitionings, Funkcional. Anal. i Priložen. 2 (1968), no. 3, 70–80 (Loose errata) (Russian). MR 0250352
  • Ja. G. Sinaĭ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (1972), no. 4(166), 21–64 (Russian). MR 0399421
  • Rufus Bowen, Markov partitions for Axiom $\textrm {A}$ diffeomorphisms, Amer. J. Math. 92 (1970), 725–747. MR 277003, DOI 10.2307/2373370
  • Rufus Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460. MR 339281, DOI 10.2307/2373793
  • William Parry and Mark Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. (2) 118 (1983), no. 3, 573–591. MR 727704, DOI 10.2307/2006982
  • Huzihiro Araki, Some contact points of mathematics and physics, Acta Appl. Math. 1 (1983), no. 1, 5–15. MR 702044, DOI 10.1007/BF02433839
  • R. Haag, N. M. Hugenholtz, and M. Winnink, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. 5 (1967), 215–236. MR 219283, DOI 10.1007/BF01646342
  • A. Connes, H. Narnhofer, and W. Thirring, Dynamical entropy of $C^\ast$ algebras and von Neumann algebras, Comm. Math. Phys. 112 (1987), no. 4, 691–719. MR 910587, DOI 10.1007/BF01225381
  • 20. A. Connes, The dynamical entropy of quantum systems, preprint.
  • James Glimm and Arthur Jaffe, Quantum physics, Springer-Verlag, New York-Berlin, 1981. A functional integral point of view. MR 628000, DOI 10.1007/978-1-4684-0121-9
  • Taro Asano, Lee-Yang theorem and the Griffiths inequality for the anisotropic Heisenberg ferromagnet, Phys. Rev. Lett. 24 (1970), 1409–1411. MR 261884, DOI 10.1103/PhysRevLett.24.1409
  • Taro Asano, Theorems on the partition functions of the Heisenberg ferromagnets, J. Phys. Soc. Japan 29 (1970), 350–359. MR 280127, DOI 10.1143/JPSJ.29.350
  • Masuo Suzuki and Michael E. Fisher, Zeros of the partition function for the Heisenberg, ferroelectric, and general Ising models, J. Mathematical Phys. 12 (1971), 235–246. MR 275824, DOI 10.1063/1.1665583
  • David Ruelle, Extension of the Lee-Yang circle theorem, Phys. Rev. Lett. 26 (1971), 303–304. MR 292441, DOI 10.1103/PhysRevLett.26.303
Similar Articles
  • Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 00A25, 82A05
  • Retrieve articles in all journals with MSC (1985): 00A25, 82A05
Additional Information
  • Journal: Bull. Amer. Math. Soc. 19 (1988), 259-268
  • MSC (1985): Primary 00A25; Secondary 82A05
  • DOI:
  • MathSciNet review: 940484