Polymer gas approach to N-body lattice systems

Journal of Statistical Physics

Volumn 96, Issue 1-2, 1999, Pages 49-68

  Procacci, Aldo ^a,b   Scoppola, Benedetto ^c  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Cluster expansion; Lattice systems; N body interaction systems; Polymer expansion

Indexed keywords

EID: 0033245918     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004564214528     Document Type: Article

References (24)

1. [BF] G. A. Battle, P. Federbush, A note on cluster expansion, tree graph identity, extra 1/N! factors!!!, Lett. Math. Phys. 8:55-97 (1984).
2. [B] D. Brydges, A Short Course on Cluster Expansion, Les Houches 1984, K. Osterwalder and R. Stora, eds. (North Holland Press, 1986).
3. [BrF] D. Brydges and P. Federbush, A new form of the Mayer expansion in classical statistical mechanics, J. Math. Phys. 19:2064-2067 (1978).
4. [C] C. Cammarota, Decay of Correlations for Infinite range Interactions in unbounded Spin Systems, Comm. Math Phys. 85:517-528 (1982).
5. [CO] M. Cassandro and E. Olivieri, Renormalization group and analiticity in one dimension: a proof of Dobrushin's theorem, Comm. Math Phys. 80:255-269 (1981).
6. [DM] R. L. Dobrushin and M. R. Martirosyan, Possibility of high temperature phase transitions due to the many-particle nature of the potential, Theor. Math. Phys. 75:443-448 (1989).
7. [vEF] A. C. D. van Enter and R. Fernandez, A remark on different norms and analticity for many-particle interactions, J. Stat. Phys. 56:965-973 (1989).
8. [GJ] J. Glimm and A. Jaffe, Quantum Physics, A Functional Integral Point of View, 2nd ed. (Springer, New York, 1987).
9. [GMs] G. Gallavotti and S. Miracle-Solé, Correlation functions for lattice systems. Comm. Math Phys. 7:274-288 (1968).
10. [GMM] G. Gallavotti, A. Martin-Löf, and S. Miracle-Solé, Some problems connected with the description of cohexistings phases at low temperature in the Ising model. In Lecture Notes in Physics, Vol. 20 (Berlin/Heidelberg/New York, Springer, 1971), pp. 162-202.
11. [GMR] G. Gallavotti, S. Miracle-Solé, and D. W. Robinson, Analiticity properties of a lattice gas, Phys. Lett. 25A:493-494 (1967).
12. [GK] C. Gruber and H. Kunz, General properties of polymer systems, Comm. Math Phys. 22:133-161 (1971).
13. [KP] R. Kotecký and D. Preiss, Cluster expansion for abstract polymer models, Comm. Math Phys. 103:491-498 (1986).
14. [K] H. Kunz, Analiticity and cluster properties of unbounded spin systems, Comm. Math Phys. 59:53-69 (1978).
15. [I] R. B. Israel, High temperature analiticity in classical lattice systems, Comm. Math Phys. 50:245-257 (1976).
16. [Ma] V. A. Malyshev, Uniform cluster estimates for lattice models, Comm. Math Phys. 64:131-157 (1979).
17. [NOZ] F. R. Nardi, E. Olivieri, and M. Zahradnik, On the Ising model with strongly anysotropic external fields, Preprint.
18. [O] E. Olivieri, On a cluster expansion for lattice spin systems: a finite size condition for the convergence, J. Stat. Phys. 50(5/6) (1988).
19. [PdLS] A. Procacci, B. N. B. de Lima, B. Scoppola, A remark on high temperature polymer expansion for lattice systems with infinite range pair interactions, Lett. Math. Phys. 45:303-322 (1998).
20. [R] D. Ruelle, Statistical Mechanics, Rigorous Results (W. A. Benjamin, New York, 1969).
21. [Ro] G. C Rota, On the foundations of the combinatorial theory. I Theory of Mœbius functions, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 2:340-368 (1964).
22. [RS] A. L. Rebenko and G. V. Shchepan'uk, The Convergence of Cluster Expansion for Continuous Systems with Many-Body Interactions, J. Stat. Phys. 88:665-689 (1997).
23. [Se] E. Seiler, Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics, Lecture Notes in Physics, Vol. 159 (Springer, New York, 1982).
24. [Si] B. Simon, The Statistical Mechanics of Lattice Gases, Vol. 1 (Princeton University Press, 1993).