Dobrushin states for classical spin systems with complex interactions

Journal of Statistical Physics

Volumn 89, Issue 5-6, 1997, Pages 895-928

  Borgs, C ^a,d   Chayes, J T ^b,d   Frohlich J ^c  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c ETH ZURICH   (Switzerland)

^d MICROSOFT RESEARCH   (United States)

Author keywords

Complex interactions; Dobrushin states; Interfaces; Pirogov Sinai theory; Surface tension

Indexed keywords

EID: 0031315755     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02764213     Document Type: Article

References (17)

1. C. Borgs, J. T. Chayes, and J. Fröhlich, Dobrushin states in quantum lattice systems, preprint, 1996.
2. C. Borgs and J. Imbrie, A unified approach to phase diagrams in field theory and statistical mechanics, Commun. Math. Phys. 123:305-328 (1989).
3. C. Borgs and J. Imbrie, Finite-size scaling and surface tension from effective one dimensional systems, Commun. Math. Phys. 145:235-280 (1992).
4. C. Borgs and R. Kotecký, A rigorous theory of finite size scaling at first order phase transitions, Journ. Stat. Phys. 61:79-119 (1990).
5. C. Borgs, R. Kotecký, and D. Ueltchi, Low temperature phase diagrams for quantum perturbations of classical spin systems. Commun. Math. Phys., in print.
6. J. Bricmont and J. Fröhlich, Statistical mechanics methods in particle structure analysis of lattice field theories II: Scalar and surface models. Commun. Math. Phys. 98:553-578 (1985).
7. D. Brydges, A short course on cluster expansions, Critical phenomena, random systems, gauge theories (Les Houches 1984) (K. Osterwalder, R. Stora, eds.), North Holland, Amsterdam, 1986.
8. N. Datta, R. Fernandez, and J. Fröhlich, Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely many ground states, J. Stat. Phys. 84:455-534 (1996).
9. R. L. Dobrushin, Gibb states describing the coexistence of phases for a three-dimensional Ising model, Theor. Prob. Appl. 17:582-600 (1972).
10. G. Gallavotti, The phase separation line in the two-dimensional Ising model, Commun. Math. Phys. 27:103-136 (1972).
11. J. Glimm and A. Jaffe, Expansions in statistical physics, Commun. Pure and Appl. Math. XXXVIII:613-630 (1985).
12. P. Holicky, R. Kotecky, and M. Zaharadnik, Rigid interlaces for lattice models at low temperatures, J. Stat. Phys. 50:755-812 (1988).
13. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Theoretical and Mathematical Physics 25:1185-1192 (1975); 26:39-49 (1976).
14. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Theoretical and Mathematical Physics 25:1185 1192 (1975); 26:39-49 (1976).
15. E. Seiler, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, Lecture notes in physics, Vol. 159, Springer Verlag, Berlin, Heidelberg, New York, 1982.
16. M. Zahradnik, An alternate version of Pirogov Sinai theory, Commun. Math. Phys. 93:559-581 (1984).
17. M. Zahradnik, Analyticity of low-temperature phase diagrams of lattice spin models, J. Stat. Phys. 47:725-755 (1988).