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References
J.L. LEBOWITZ, Statistical Mechanics — A Review of Selected Rigorous Results, An. Rev. of Chem. Phys., 389 (1968). This article contains extensive references through 1967 for all the subjects covered in these lectures.
The Equilibrium Theory of Classical Fluids, H.L. FRISCH and J.L. LEBOWITZ eds, W.A. Benjamin, N.Y. 1964. Contains reprints and original articles.
D. RUELLE, Statistical Mechanics, W.A. Benjamin, New York, 1969.
Critical Phenomena and Phase Transitions, Vols. 1–6, C. DOMB and M.S. GREEN, eds., Academic Press, 1971. Contains many articles relevant to lectures. See in particular article by R. GRIFFITHS.
Proceedings of the 1971 Battelle Rencontres on Statistical Mechanics, A. LENARD, Ed., Springer Verlag, Lecture Notes in Physics, 1972.
M.E. FISHER, Arch. Ratl. Mech. Anal. 17, 377 (1964). This paper contains a complete detailed description of the thermodynamic limit of the free energy in both canonical and grand canonical ensemble.
J.L. LEBOWITZ and E.H. LIEB, Phys. Rev, Lett. E.H. LIEB and J.L. LEBOWITZ, Adv. in Math. 1973. These articles prove the existence of the thermodynamic limit for Coulomb Systems.
M.E. FISHER and J.L. LEBOWITZ, Comm. Math. Phys. discuss periodic boundary conditions for classical systems.
J.L. LEBOWITZ and O. PENROSE, J. Math. Phys. 7, 98 (1966)
O. PENROSE and J.L. LEBOWITZ, J. Stat. Phys. 3, 211 (1971). The first of these papers deals with equilibrium properties and the second with metastable states.
P.C. HEMMER and J.L. LEBOWITZ, Systems with Weak Long-Range Potentials, in Vol. 5 of Reference 1.4. This paper contains a review of both rigorous and non-rigorous results.
O. PENROSE and J.L. LEBOWITZ. Towards a Rigorous Molecular Theory of Metastability; review article, to appear.
G.A. Baker, Phys. Rev. 122, 1477 (1961). First use of van der Waals limit, γ→0.
M. KAC, G.E. UHLENBECK and P.C. HEMMER, J. Math. Phys. 4, 216 (1963); 4, 229 (1963); 5, 60 (1964). Exact derivation of van der Waals' equation for a special system.
N.G. van Kampen, Phys. Rev. 135A, 362 (1964); Physica 48, 313 (1970). Basic idea of dividing system into cells containing many particles yet small compared to γ-1. Discusses surface tension.
E. LIEB, J. Math. Phys. 7, 1016 (1966). Extension of results to quantum systems.
D.J. GATES and O. PENROSE, Comm. Math. Phys. 15, 255; 16, 231; 17, 194 (1970). Generalization of results to oscillatory long range potentials plus other things.
K. MILLARD and L. LUND, J. Stat. Phys. 8, 225 (1973). Completes PENROSE and LEBOWITZ argument bounding ascape rate λ to all of metastable region.
J.L. LEBOWITZ, Uniqueness, Analyticity and Decay Properties of Correlations in Equilibrium Systems, Proceedings of the Kyoto Conference on Math.ys. K. Araki, Ed. Springer Verlag, 1975. Contains summary of known results for spin- Ising systems.
C.N. YANG and T.D. LEE and companion paper by T.D. LEE and C.N. YANG, Phys. Rev. 87, 410 (1952). They introduce analysis of zeros of Ξ (z, Λ) and prove “circle” theorem for ferromagnetic spin systems.
C. NEWMAN, Comm. Pure and Appl. Math., 1974, generalizes LEE-YANG circle theorem.
S.A. PIROGOV and Ya.G. SINAI, Phase Transitions of the First Kind for Small Perturbations of the Ising Model, Func. Anal. Appl. 21, 8 (1974). They prove phase transitions at some value of magnetic field h when “small” but otherwise quite arbitrary many spin interactions are added to ferromagnetic pair interactions.
J. FROHLICH, B. SIMON and T. SPENCER, Phase Transitions and Continuous Symmetry Breaking, Phys. Rev. Lett. (1976) and preprint. Prove phase transitions for n-component spin systems with nearest neighbor ferromagnetic interactions in ν ⩾ 3 dimensions.
F. DYSON, E.H. LIEB and B. SIMON, preprint prove phase transition for quantum spin systems in v ⩾ 3.
J.L. LEBOWITZ and E. PRESUTTI, Statistical Mechanics of Systems of Unbounded spins, to appear in Comm. Math. Phys.
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Lebowitz, J.L. (1976). Statistical mechanics of equilibrium systems: Some rigorous results. In: Brey, J., Jones, R.B. (eds) Critical Phenomena. Lecture Notes in Physics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034510
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DOI: https://doi.org/10.1007/BFb0034510
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