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Is our mathematics natural? The case of equilibrium statistical mechanics
Author(s):
David
Ruelle
Journal:
Bull. Amer. Math. Soc.
19
(1988),
259-268.
MSC (1985):
Primary 00A25;
Secondary 82A05
MathSciNet review:
940484
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Additional information
References:
- 1.
- P. Cartier, La pratique—et les pratiques—des mathématiques, Encyclopédie Philosophique Universelle, Presses Univ. de France, Paris, 1988 (to appear).
- 2.
- E. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13 (1960), 1-14. MR 824292
- 3.
- D. Ruelle, Statistical mechanics. Rigorous results, Benjamin, New York, 1969. MR 289084
- 4.
- R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math., vol. 470, Springer-Verlag, Berlin, 1975. MR 442989
- 5.
- D. Ruelle, Thermodynamic formalism, Encyclopedia of Math. and its Appl., vol. 5, Addison-Wesley, Reading, Mass., 1978. MR 511655
- 6.
- R. Israel, Convexity in the theory of lattice gases, Princeton Univ. Press, Princeton, N. J., 1979. MR 517873
- 7.
- Ia. G. Sinai, Theory of phase transitions: Rigorous results, Pergamon, Oxford, 1982. MR 691854
- 8.
- D. Ruelle, Correlation functionals, J. Math. Phys. 6 (1965), 201-220. MR 201174
- 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.
- 10.
- 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 (1952), 410-419. MR 53029
- 11.
- la. G. Sinai, Markov partitions and C-diffeomorphisms, Funktsional Anal. i Prilozhen 2 No. 1 (1968), 64-89; English transl., Functional Anal. Appl. 2 (1968), 61-82. MR 233038
- 12.
- la. G. Sinai, Construction of Markov partitions, Funktsional Anal. i Prilozhen 2 No. 3 (1968), 70-80; English transl., Functional Anal. Appl. 2 (1968), 245-253. MR 250352
- 13.
- la. G. Sinai, Gibbs measures in ergodic theory, Uspekhi Mat. Nauk 27 No. 4 (1972), 21-64; English transl., Russian Math. Surveys 27 No. 4 (1972), 21-69. MR 399421
- 14.
- R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725-747. MR 277003
- 15.
- R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429-459. MR 339281
- 16.
- W. Parry and M. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math. (2) 118 (1983), 573-591. MR 727704
- 17.
- H. Araki, Some contact points of mathematics and physics, Invited talk, First Pan-African Congress of Mathematicians, Rabat, 1976 (Zi F, Bielefeld, preprint). MR 702044
- 18.
- 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
- 19.
- A. Connes, H. Narnhofer and W. Thirring, Dynamical entropy of C* algebras and von Neumann algebras, Comm. Math. Phys. 112 (1987), 691-719. MR 910587
- 20.
- A. Connes, The dynamical entropy of quantum systems, preprint.
- 21.
- J. Glimm and A. Jaffe, Quantum physics: a functional integral point of view, Springer-Verlag, New York, 1981. MR 628000
- 22.
- T. Asano, Lee-Yang theorem and the Griffiths inequality for the anisotropic Heisenberg ferromagnet, Phys. Rev. Letters 24 (1970), 1409-1411. MR 261884
- 23.
- T. Asano, Theorems on the partition functions of the Heisenberg ferromagnets, J. Phys. Soc. Japan 29 (1970), 350-359. MR 280127
- 24.
- M. Suzuki and M. E. Fisher, Zeros of the partition function for the Heisenberg, ferroelectric, and general Ising models, J. Math. Phys. 12 (1971), 235-246. MR 275824
- 25.
- D. Ruelle, Extension of the Lee-Yang circle theorem, Phys. Rev. Letters 26 (1971), 303-304. MR 292441
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Additional Information:
DOI:
10.1090/S0273-0979-1988-15634-0
PII:
S 0273-0979(1988)15634-0
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