Some problems in statistical mechanics that I would like to see solved

Physica A: Statistical Mechanics and its Applications

Volumn 263, Issue 1-4, 1999, Pages 491-499

  Lieb, Elliott H ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Quantum electrodynamics; Quantum mechanics; Statistical mechanics; Thermodynamics

Indexed keywords

EID: 0040841841     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00517-2     Document Type: Article

References (18)

1. E.H. Lieb, Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967); Exact Solution of the F Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967); Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967); The Residual Entropy of Square. Ice, Phys. Rev. 162, 162-172 (1967).
2. E.H. Lieb, Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967); Exact Solution of the F Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967); Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967); The Residual Entropy of Square. Ice, Phys. Rev. 162, 162-172 (1967).
3. E.H. Lieb, Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967); Exact Solution of the F Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967); Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967); The Residual Entropy of Square. Ice, Phys. Rev. 162, 162-172 (1967).
4. E.H. Lieb, Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967); Exact Solution of the F Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967); Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967); The Residual Entropy of Square. Ice, Phys. Rev. 162, 162-172 (1967).
5. E.H. Lieb and F.Y. Wu, Two Dimensional Ferroelectric Models, in Phase Transitions and Critical Phenomena, C. Domb and M. Green eds., vol. 1, Academic Press 331-490 (1972).
6. These arguments can be found in J. Glimm and A. Jaffe, Quantum Physics, Springer (1987). The spin-space reflection positivity is in E.H. Lieb, Two Theorems on the Hubbard Model, Phys. Rev. Lett. 62, 1201-1204 (1989). Errata 62, 1927 (1989).
7. These arguments can be found in J. Glimm and A. Jaffe, Quantum Physics, Springer (1987). The spin-space reflection positivity is in E.H. Lieb, Two Theorems on the Hubbard Model, Phys. Rev. Lett. 62, 1201-1204 (1989). Errata 62, 1927 (1989).
8. E.H. Lieb and J. Yngvason, The Physics and Mathematics of the Second Law of Thermodynamics, Physics Reports (in press).
9. E.H. Lieb and J. Yngvason, A guide to Entropy and the Second Law of Thermodynamics, Notices of the Amer. Math. Soc. 45, 571-581 (1998).
10. T. Kennedy, E.H. Lieb and S. Shastry, The XY Model has Long-Range Order for all Spins and all Dimensions Greater than One, Phys. Rev. Lett. 61, 2582-2584 (1988).
11. T. Kennedy and E.H. Lieb, An Itinerant Electron Model with Crystalline or Magnetic Long Range Order, Physica 138A, 320-358 (1986).
12. T. Kennedy and E.H. Lieb, Proof of the Peierls Instability in One Dimension, Phys. Rev. Lett. 59, 1309-1312 (1987); E.H. Lieb and B. Nachtergaele, The Stability of the Peierls Instability for Ring Shaped Molecules, Phys. Rev. B 51, 4777-4791 (1995).
13. T. Kennedy and E.H. Lieb, Proof of the Peierls Instability in One Dimension, Phys. Rev. Lett. 59, 1309-1312 (1987); E.H. Lieb and B. Nachtergaele, The Stability of the Peierls Instability for Ring Shaped Molecules, Phys. Rev. B 51, 4777-4791 (1995).
14. K. Hepp and E.H. Lieb, The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion, in Dynamical Systems, Battelle 1974 Rencontres, Springer Lecture Notes in Physics 38, 178-208 (1975); Phase Transition in Reservoir Driven Open Systems with Applications to Lasers and Superconductors, Helv. Phys. Acta 46, 573-602 (1973). Constructive Macroscopic Quantum Electrodynamics, in Constructive Quantum Field Theory, Proceedings of the 1973 Erice Summer School, G. Velo and A. Wightman, eds., Springer Lecture Notes in Physics 25, 298-316 (1973).
15. K. Hepp and E.H. Lieb, The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion, in Dynamical Systems, Battelle 1974 Rencontres, Springer Lecture Notes in Physics 38, 178-208 (1975); Phase Transition in Reservoir Driven Open Systems with Applications to Lasers and Superconductors, Helv. Phys. Acta 46, 573-602 (1973). Constructive Macroscopic Quantum Electrodynamics, in Constructive Quantum Field Theory, Proceedings of the 1973 Erice Summer School, G. Velo and A. Wightman, eds., Springer Lecture Notes in Physics 25, 298-316 (1973).
16. K. Hepp and E.H. Lieb, The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion, in Dynamical Systems, Battelle 1974 Rencontres, Springer Lecture Notes in Physics 38, 178-208 (1975); Phase Transition in Reservoir Driven Open Systems with Applications to Lasers and Superconductors, Helv. Phys. Acta 46, 573-602 (1973). Constructive Macroscopic Quantum Electrodynamics, in Constructive Quantum Field Theory, Proceedings of the 1973 Erice Summer School, G. Velo and A. Wightman, eds., Springer Lecture Notes in Physics 25, 298-316 (1973).
17. W.E. Thirring, ed. the Stability of Matter: From Atoms to Stars, Selecta of E.H. Lieb, 2nd edition, Springer (1997).
18. E.H. Lieb and M. Loss, Remarks about the Ultraviolet Problem in QED, in preparation.