Phase Transitions and Topology Changes in Configuration Space

Journal of Statistical Physics

Volumn 111, Issue 5-6, 2003, Pages 1091-1123

  Casetti, Lapo ^a   Pettini, Marco ^a,b   Cohen, E G D ^c  

^a INFM   (Italy)

^b INAF OSSERVATORIO ASTROFISICO DI ARCETRI   (Italy)

^c ROCKEFELLER UNIVERSITY   (United States)

Author keywords

Configuration space; Mean field models; Phase transitions; Topology

Indexed keywords

EID: 0037259303     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023044014341     Document Type: Article

References (26)

1. C. N. Yang and T. D. Lee, Phys. Rev. 87:404 (1952); T. D. Lee and C. N. Yang, Phys. Rev. 87:410 (1952).
2. C. N. Yang and T. D. Lee, Phys. Rev. 87:404 (1952); T. D. Lee and C. N. Yang, Phys. Rev. 87:410 (1952).
3. D. Ruelle, Statistical Mechanics: Rigorous Results (World Scientific, Singapore, 1999).
4. See, e.g., H. O. Georgii, Gibbs Measures and Phase Transitions (de Gruyter, New York, 1988).
5. D. H. E. Gross, Microcanonical Thermodynamics, Phase Transitions in Small Systems (World Scientific, Singapore, 2001).
6. L. Caiani, L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. Lett. 79:4361 (1997).
7. R. Franzosi, L. Casetti, L. Spinelli, and M. Pettini, Phys. Rev. E 60:R5009 (1999).
8. L. Casetti, E. G. D. Cohen, and M. Pettini, Phys. Rev. Lett. 82:4160 (1999).
9. R. Franzosi, M. Pettini, and L. Spinelli, Phys. Rev. Lett. 84:2774 (2000).
10. L. Casetti, M. Pettini, and E. G. D. Cohen, Phys. Rep. 337:237 (2000).
11. M. Cerruti-Sola, C. Clementi, and M. Pettini, Phys. Rev. E 61:5111 (2000).
12. M. Nakahara, Geometry, Topology and Physics (Adam Hilger, Bristol, 1991).
13. J. Milnor, Morse Theory (Princeton University Press, Princeton, 1951).
14. R. S. Palais and C. Terng, Critical Point Theory and Submanifold Geometry (Springer, NY, 1988).
15. R. Franzosi, M. Pettini, and L. Spinelli, cond-mat/0104110, and in preparation.
16. L. Casetti, E. G. D. Cohen, and M. Pettini, Phys. Rev. E 65:036112 (2002).
17. M. Antoni and S. Ruffo, Phys. Rev. E 52:2361 (1995).
18. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).
19. P. G. Debenedetti and F. H. Stillinger, Nature 410:259 (2001).
20. L. Angelani et al., Phys. Rev. Lett. 85:5356 (2000); A. Cavagna, I. Giardina, and G. Parisi, J. Phys. A: Math. Gen. 34:5317 (2001); T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88:055502 (2002); R. M. C. de Almeida, N. Lemke, and I. A. Campbell, cond-mat/0003351.
21. L. Angelani et al., Phys. Rev. Lett. 85:5356 (2000); A. Cavagna, I. Giardina, and G. Parisi, J. Phys. A: Math. Gen. 34:5317 (2001); T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88:055502 (2002); R. M. C. de Almeida, N. Lemke, and I. A. Campbell, cond-mat/0003351.
22. L. Angelani et al., Phys. Rev. Lett. 85:5356 (2000); A. Cavagna, I. Giardina, and G. Parisi, J. Phys. A: Math. Gen. 34:5317 (2001); T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88:055502 (2002); R. M. C. de Almeida, N. Lemke, and I. A. Campbell, cond-mat/0003351.
23. L. Angelani et al., Phys. Rev. Lett. 85:5356 (2000); A. Cavagna, I. Giardina, and G. Parisi, J. Phys. A: Math. Gen. 34:5317 (2001); T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi, Phys. Rev. Lett. 88:055502 (2002); R. M. C. de Almeida, N. Lemke, and I. A. Campbell, cond-mat/0003351.
24. B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modem Geometry-Methods and Applications (Parts I, II, and III, Springer, NY, 1985).
25. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, 1996).
26. M. Spivak, Comprehensive Introduction to Differential Geometry (Publish or Perish, Berkeley, 1979).