Phase diagram of Ising systems with additional long range forces

Communications in Mathematical Physics

Volumn 189, Issue 2, 1997, Pages 287-298

  Bodineau, T ^a   Presutti, E ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008983832     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050202     Document Type: Article

References (19)

1. Alberti, G., Bellettini, G., Cassandro, M., Presutti, E.: Surface tension in Ising system with Kac potentials. J. Stat. Phys. 82, 743-796 (1996)
2. Cassandro, M., Presutti, E.: Phase transitions in Ising systems with long but finite range. Markov Processes and Related Fields 2, 241-262 (1996)
3. DeMasi, A., Orlandi, E., Presutti, E., Triolo, L.: Glauber evolution with Kac potentials. I. Mesoscopic and macroscopic limits, interface dynamics. Nonlinearity 7, 1-67 (1994)
4. Dobrushin, R.L.: Prescribing a system of random variables by the help of conditional distributions. Theor. Prob. and Appl. 15, N 3, 469-497 (1970)
5. Dobrushin, R.L., Shlosman, S.B.: Constructive criterion for the uniqueness of Gibbs fields. Statistical Physics and Dynamical Systems, Basel-Boston: Birkhäuser, 1985
6. Dobrushin, R.L., Shlosman, S.B.: Completely analytical Gibbs fields. Statistical Physics and Dynamical Systems, Basel-Boston: Birkhäuser, 1985
7. Dobrushin, R.L., Shlosman, S.B.: Completely analytical interactions: Constructive description. J. Stat. Phys. 46, 983-1014 (1987)
8. Dobrushin, R.L., Shlosman, S.B.: The problem of translation invariance of Gibbs states at low temperatures. In: S.P. Novikov (ed), Soviet Scientific Reviews C, Math. Phys. 5, London: Harwood Ac. Publ, 1985, pp. 53-196
9. Ellis, R.: Entropy large deviations and statistical mechanics. Berlin-Heidelberg-New York: Springer-Verlag, 1985
10. Higuchi, Y.: Coexistence of infinite *-cluster. Ising Percolation in two dimensions. Prob. Theor. Rel. Fields 97, 1-34 (1993)
11. Kac, M., Uhlenbeck, G., Hemmer, P.C.: On the Van der Waals theory of vapor-liquid equilibrium: I. Discussion of a one dimensional model. J. Math. Phys. 4, 216-228 (1963); II. Discussion of the distribution functions. J. Math. Phys. 4, 229-247 (1963); III. Discussion of the critical region. J. Math. Phys. 5, 60-74 (1964)
12. Kac, M., Uhlenbeck, G., Hemmer, P.C.: On the Van der Waals theory of vapor-liquid equilibrium: I. Discussion of a one dimensional model. J. Math. Phys. 4, 216-228 (1963); II. Discussion of the distribution functions. J. Math. Phys. 4, 229-247 (1963); III. Discussion of the critical region. J. Math. Phys. 5, 60-74 (1964)
13. Kac, M., Uhlenbeck, G., Hemmer, P.C.: On the Van der Waals theory of vapor-liquid equilibrium: I. Discussion of a one dimensional model. J. Math. Phys. 4, 216-228 (1963); II. Discussion of the distribution functions. J. Math. Phys. 4, 229-247 (1963); III. Discussion of the critical region. J. Math. Phys. 5, 60-74 (1964)
14. Lebowitz, J., Penrose, O.: Rigorous treatment of the Van der Waals Maxwell theory of the liquid vapour transition. J. Math. Phys. 7, 98-113 (1966)
15. Martinelli, F., Olivieri, E.: Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case. Commun. Math. Phys. 161, 447-486 (1994); II. The general case. Commun. Math. Phys. 161, 487-514 (1994)
16. Martinelli, F., Olivieri, E.: Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case. Commun. Math. Phys. 161, 447-486 (1994); II. The general case. Commun. Math. Phys. 161, 487-514 (1994)
17. Martinelli, F., Olivieri, E., Schonmann, R.: For 2-D lattice spin systems weak mixing implies strong mixing. Commun. Math. Phys. 165, 33-47 (1994)
18. Schonmann, R., Shlosman, S.: Complete analyticity for 2D Ising completed. Commun. Math. Phys. 170, 453-482 (1995)
19. Zahradnik, M.: A short course on the Pirogov-Sinai theory. Roma Tor Vergata, Feb. 1996