The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Aizenman, M; Chayes, J; Chayes, L; Newman, C. Discontinuity of the magnetization in one-dimensional 1/|x-y|^2 Ising and Potts models, J. Statist. Phys. 50 (1988), 1--40.
  2. Georgii, Hans-Otto. Gibbs measures and phase transitions. de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 1988. xiv+525 pp. ISBN: 0-89925-462-4 MR0956646 (89k:82010)
  3. Georgii, Hans-Otto; Häggström, Olle; Maes, Christian. The random geometry of equilibrium phases. Phase transitions and critical phenomena, Vol. 18, 1--142, Phase Transit. Crit. Phenom., 18, Academic Press, San Diego, CA, 2001. MR2014387 (2004h:82022)
  4. Grimmett, Geoffrey. The random-cluster model. Springer, 2006.
  5. Häggström, O. Random-cluster representations in the study of phase transitions. Markov Process. Related Fields 4 (1998), no. 3, 275--321. MR1670023 (2000e:60182)
  6. Häggström, Olle. Positive correlations in the fuzzy Potts model. Ann. Appl. Probab. 9 (1999), no. 4, 1149--1159. MR1728557 (2001b:60118)
  7. Häggström, Olle. Markov random fields and percolation on general graphs. Adv. in Appl. Probab. 32 (2000), no. 1, 39--66. MR1765172 (2001g:60246)
  8. Häggström, Olle. Is the fuzzy Potts model Gibbsian? Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 5, 891--917. MR1997217 (2005f:82049)
  9. Häggström, Olle; Külske, Christof. Gibbs properties of the fuzzy Potts model on trees and in mean field. Markov Processes and Related Fields 10 (2004), 477--506.
  10. Kahn, Jeff; Weininger, Nicholas. Positive association in the fractional fuzzy Potts model. Ann. Probab. 35 (2007), no. 6, 2038--2043. MR2353381 (2008k:60245)
  11. Künsch, H; Geman, S; Kehagias, A. Hidden Markov random fields. Ann. Appl. Probab. 5 (1995), 577--602.
  12. Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231 (86e:60089)
  13. Liggett, Thomas M.; Steif, Jeffrey E. Stochastic domination: the contact process, Ising models and FKG measures. Ann. Inst. H. Poincaré Probab. Statist. 42 (2006), no. 2, 223--243. MR2199800 (2007i:60131)
  14. Maes, Christian; Vande Velde, Koen. The fuzzy Potts model. J. Phys. A 28 (1995), no. 15, 4261--4270. MR1351929 (96i:82022)
  15. Schonmann, Roberto H.; Tanaka, Nelson I. Lack of monotonicity in ferromagnetic Ising model phase diagrams. Ann. Appl. Probab. 8 (1998), no. 1, 234--245. MR1620366 (99b:60171)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.