Table of Contents
Physics Research International
Volume 2011, Article ID 437093, 5 pages
http://dx.doi.org/10.1155/2011/437093
Research Article

Microcanonical Entropy of the Infinite-State Potts Model

Solid State Physics, Lund University, P.O. Box 118, 221 00 Lund, Sweden

Received 24 March 2011; Revised 2 September 2011; Accepted 7 September 2011

Academic Editor: Ashok Chatterjee

Copyright © 2011 Jonas Johansson and Mats-Erik Pistol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. L. Hill, “Thermodynamics of small systems,” The Journal of Chemical Physics, vol. 36, no. 12, pp. 3182–3197, 1962. View at Google Scholar · View at Scopus
  2. P. Borrmann, O. Mülken, and J. Harting, “Classification of phase transitions in small systems,” Physical Review Letters, vol. 84, no. 16, pp. 3511–3514, 2000. View at Google Scholar · View at Scopus
  3. F. Gulminelli and P. Chomaz, “Critical behavior in the coexistence region of finite systems,” Physical Review Letters, vol. 82, no. 7, pp. 1402–1405, 1999. View at Google Scholar · View at Scopus
  4. P. Chomaz and F. Gulminelli, “First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem,” Physica A, vol. 330, no. 3-4, pp. 451–458, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. P. Chomaz and F. Gulminelli, “The challenges of finite-system statistical mechanics,” European Physical Journal A, vol. 30, no. 1, pp. 317–331, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. D. H. E. Gross, A. Ecker, and X. Z. Zhang, “Microcanonical thermodynamics of first order phase transitions studied in the Potts model,” Annalen der Physik, vol. 5, no. 5, pp. 446–452, 1996. View at Google Scholar · View at Scopus
  7. D. H. E. Gross, “A new thermodynamics from nuclei to stars,” Entropy, vol. 6, no. 1, pp. 158–179, 2004. View at Google Scholar · View at Scopus
  8. D. H. E. Gross and J. F. Kenney, “The microcanonical thermodynamics of finite systems: the microscopic origin of condensation and phase separations, and the conditions for heat flow from lower to higher temperatures,” Journal of Chemical Physics, vol. 122, no. 22, Article ID 224111, pp. 1–8, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  9. L. Mittag and M. J. Stephen, “Mean-field theory of the many component Potts model,” Journal of Physics A, vol. 7, no. 9, pp. L109–L112, 1974. View at Publisher · View at Google Scholar · View at Scopus
  10. P. A. Pearce and R. B. Griffiths, “Potts model in the many-component limit,” Journal of Physics A, vol. 13, no. 6, pp. 2143–2148, 1980. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Y. Wu, “The Potts model,” Reviews of Modern Physics, vol. 54, no. 1, pp. 235–268, 1982. View at Publisher · View at Google Scholar · View at Scopus
  12. M. S. S. Challa, D. P. Landau, and K. Binder, “Finite-size effects at temperature-driven first-order transitions,” Physical Review B, vol. 34, no. 3, pp. 1841–1852, 1986. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Johansson, “Monte Carlo investigation of the phase transition in the 2D Potts model with open boundary conditions,” Physics Letters Section A, vol. 372, no. 42, pp. 6301–6304, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. Jiang and J. A. Glazier, “Extended large-Q Potts model simulation of foam drainage,” Philosophical Magazine Letters, vol. 74, no. 2, pp. 119–128, 1996. View at Google Scholar · View at Scopus
  15. F. Y. Wu, “The infinite-state potts model and restricted multidimensional partitions of an integer,” Mathematical and Computer Modelling, vol. 26, no. 8–10, pp. 269–274, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. F. Y. Wu, G. Rollet, H. Y. Huang, J. M. Maillard, C. K. Hu, and C. N. Chen, “Directed compact lattice animals, restricted partitions of an integer, and the infinite-state potts model,” Physical Review Letters, vol. 76, no. 2, pp. 173–176, 1996. View at Google Scholar · View at Scopus
  17. F. Wang and D. P. Landau, “Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram,” Physical Review E, vol. 64, no. 5, Article ID 056101, pp. 1–16, 2001. View at Google Scholar · View at Scopus
  18. Sμ, σ, and ψ all depend on the three variables E, N, and q. For a compact notation we only write the E dependence explicitly.
  19. R. C. Read, “An introduction to chromatic polynomials,” Journal of Combinatorial Theory, vol. 4, no. 1, pp. 52–71, 1968. View at Google Scholar · View at Scopus
  20. R. Shrock, “Chromatic polynomials and their zeros and asymptotic limits for families of graphs,” Discrete Mathematics, vol. 231, no. 1–3, pp. 421–446, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. R. Shrock and S. H. Tsai, “Asymptotic limits and zeros of chromatic polynomials and ground-state entropy of Potts antiferromagnets,” Physical Review E, vol. 55, no. 5 A, pp. 5165–5178, 1997. View at Google Scholar · View at Scopus
  22. R. Diestel, Graph Theory, Springer, Heidelberg, German, 2005.
  23. With convex we mean strictly convex. A function, f, is strictly convex if for any two points, x and y, and any 0t1, we have f(tx+(1t)y)<tf(x)+(1t)f(y). If f is convex, then f is concave. A linear function is concave (and convex but neither strictly convex, nor strictly concave).
  24. R. J. Baxter, “Potts model at the critical temperature,” Journal of Physics C, vol. 6, no. 23, pp. L445–L448, 1973. View at Publisher · View at Google Scholar · View at Scopus