User menu

A note on the Ising model in high dimensions

Bibliographic reference Bricmont, Jean ; Kesten, H. ; Lebowitz, J.L. ; Schonmann, R.H.. A note on the Ising model in high dimensions. In: Communications in Mathematical Physics, Vol. 122, no. 4, p. 597-607 (1989)
Permanent URL http://hdl.handle.net/2078.1/66342
  1. Aizenman, M., Fernandez, R.: On the critical behavior of the magnetization in high-dimensional Ising models. J. Stat. Phys.44, 395?454 (1986)
  2. Billingsley, P.: Probability and measure, 2nd ed. New York: John Wiley 1986
  3. Brout, R.: Statistical mechanical theory of ferromagnetism high density behavior. Phys. Rev.118, 1009?1019 (1960)
  4. Bricmont, J., Fontaine, J. R.: Perturbation about the mean field critical point. Commun. Math. Phys.86, 337?362 (1982)
  5. Ellis, R.: Entropy, large deviations and statistical mechanics. Berlin, Heidelberg, New York: Springer 1985
  6. Fisher, M.: Critical temperatures of anisotropic Ising lattices. II. General upper bounds. Phys. Rev.162, 480?485 (1967)
  7. Fr�hlich, J., Israel, R., Lieb, E. H., Simon, B.: Phase transition and reflexion positivity. I. General theory and long range lattice models. Commun. Math. Phys.62, 1?34 (1978)
  8. Fr�hlich, J., Simon, B., Spencer, T.: Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys.50, 79?85 (1976)
  9. Griffiths, R. B.: Correlations in Ising ferromagnets. III. Commun. Math. Phys.6, 121?127 (1967)
  10. Kesten, H.: Asymptotics in high dimension for percolation. To appear in Festschrift in honor of J. M. Hammersley
  11. Kesten, H.: Asymptotics in high dimension for the Fortuin-Kasteleyn random cluster model. To appear in Festschrift in honor of T. E. Harris
  12. Kesten, H., Schonmann, R. H.: Behavior in large dimensions of the Potts and Heisenberg models. To appear in Rev. Math. Phys.
  13. Lebowitz, J. L., Martin-L�f, A.: On the uniqueness of the equilibrium state for Ising spin systems. Commun. Math. Phys.25, 276?282 (1972)
  14. Lebowitz, J. L., Penrose, O.: Rigorous treatment of the van der Waals-Maxwell theory of liquid-vapor transition. J. Math. Phys.7, 98?113 (1966)
  15. Newman, C. M.: Shock waves and mean field bounds. Concavity and analyticity of the magnetization at low temperatures. Appendix to Percolation theory: A selective survey of rigorous results, pp. 147?167. In Advances in multiphase flow and related problems. Papanicolaou, G., (ed.): SIAM 1987
  16. Pearce, P. A.: Mean field bounds on the magnetization for ferromagnetic spin models. J. Stat. Phys.25, 309?320 (1981)
  17. Preston, C. J.: An application of the GHS inequalities to show the absence of phase transition for Ising spin systems. Commun. Math. Phys.35, 253?255 (1974)
  18. Pearce, P. A., Thompson, C. J.: The high density limit for lattice spin models. Commun. Math. Phys.58, 131?138 (1978)
  19. Ruelle, D.: Thermodynamic formalism. Reading, MA: Addison Wesley 1978
  20. Schonmann, R. H., Vares, M. E.: The survival of the large dimensional basic contact process. Probab. Th. Rel. Fields72, 387?393 (1986)
  21. Simon, B.: Mean field upper bound on the transition temperature in multicomponent ferromagnets. J. Stat. Phys.22, 491?493 (1980)
  22. Slawny, J.: On the mean field theory bound on the magnetization. J. Stat. Phys.32, 375?388 (1983)
  23. Thompson, C. J.: Upper bounds for Ising model correlation functions. Commun. Math. Phys.24, 61?66 (1971)
  24. Thompson, C. J.: Mathematical statistical mechanics. Princeton, NJ: Princeton University Press (1972)
  25. Thompson, C. J.: Ising model in the high density limit. Commun. Math. Phys.36, 255?262 (1974)
  26. Tasaki, H., Hara, T.: Mean field bound and GHS inequality. J. Stat. Phys.35, 99?107 (1984)
  27. Vigfusson, J. O.: New upper bounds for the magnetization in ferromagnetic one-component systems. Lett. Math. Phys.10, 71?77 (1985)