Variational principle for some renormalized measures

Journal of Statistical Physics

Volumn 96, Issue 1-2, 1999, Pages 109-133

  Lefevere, R ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Gibbs measures; Renormalization group pathologies; Variational principle; Weakly Gibbsian

Indexed keywords

EID: 0033245915     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004568315437     Document Type: Article

References (22)

1. 1. J. Bricmont, A. Kupiainen, and R. Lefevere, Renormalization Group pathologies and the definition of Gibbs states, Commun. Math. Phys. 194:359-388 (1998).
2. 2. R. L. Dobrushin, Lecture given at the workshop "Probability and Physics." Renkum, Holland, 28 August-1 September (1995).
3. 3. C. Domb and M. S. Green, Eds., Phase Transitions and Critical Phenomena. Vol. 6 (Academic Press, New York, 1976).
4. 4. R. Fernández and C.-Ed. Pfister, Global specifications and non-quasilocality of projections of Gibbs measures, EPFL preprint (1996).
5. 5. H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, Vol. 9 ( (Walter de Gruyter, Berlin/New York, 1988).
6. 6. R. B. Griffiths, Nonanalytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23:17 (1969).
7. 7. R. B. Griffith and P. A. Pearce, Position-space renormalization-group transformations: Some proofs and some problems, Phys. Rev. Lett. 41:917-920 (1978).
8. 8. R. B. Griffiths and P. A. Pearce, Mathematical properties of position-space renormalization-group transformations, J. Stat. Phys. 20:499-545 (1979).
9. 9. R. B. Israel, Banach algebras and Kadanoff transformations, Random Fields (Esztergom, 1979), Vol. II, J. Fritz, J. L. Lebowitz, and D. Szász, eds. (North-Holland, Amsterdam, 1981), pp. 593-608.
10. 10. H. Künsch, Almost sure entropy and the variational principle for random fields with unbounded state space, Z. Wahrscheinlichkeitstheorie Verw. Geb. 58:69-85 (1981).
11. 11. J. L. Lebowitz and E. Presutti, Statistical Mechanics of systems of unbounded spins, Commun. Math. Phys. 50:195-218 (1976).
12. 12. J. Lörinczi and C. Maes. Weakly Gibbsian measures tor lattice spins systems, J. Stat. Phys. 89:561-579 (1997).
13. 13. J. Lörinczi and K. Vande Velde, A note on the projection of Gibbs measures, J. Stat. Phys. 77:881-887 (1994).
14. 14. C. Maes and K. Vande Velde. Relative energies for non-Gibbsian states, Commun. Math. Phys. 189:277-286 (1997).
15. 15. F. Martinelli and E. Olivieri, Some remarks on pathologies of renormalization-group transformations, J. Stat. Phys. 72:1169-1177 (1993).
16. 16. F. Martinelli and E. Olivieri, Instability of renormalization-group pathologies under decimation, J. Stat. Phys. 79:25-42 (1995).
17. 17. R. H. Schonmann, Projections of Gibbs measures may be non-Gibbsian, Comm. Math. Phys. 124:1-7 (1989).
18. 18. A. C. D. van Enter, Ill-defǐned block-spin transformations at arbitrarily high temperatures, J. Stat. Phys. 83:761-765 (1996).
19. 19. A. C. D. van Enter, R. Fernández, and R. Kotecký, Pathological behavior of renormalization group maps at high fields and above the transition temperature, J. Stat. Phys. 79:969-992 (1995).
20. 20. A. C. D. van Enter. R. Fernández, and A. D. Sokal, Renormalization transformations in the vicinity of first-order phase transitions: What can and cannot go wrong, Phys. Rev. Lett. 66:3253-3256 (1991).
21. 21. A. C. D. van Enter, R. Fernández, and A. D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory, J. Stat. Phys. 72:879-1167 (1993).
22. 22. A. C. D. van Enter and J. Lörinczi, Robustness of the non-Gibbsian property: some examples. University of Groningen preprint, 1995, J. Phys. A, Math. and Gen. 29:2465-2473 (1996).