- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Comparison of complete scaling and a field-theoretic treatment of asymmetric fluid criticality

C. E. Bertrand1,*, J. F. Nicoll2, and M. A. Anisimov1

  • 1Institute for Physical Science & Technology, and Department of Chemical & Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, USA
  • 2Institute for Defense Analysis, Alexandria, Virginia 22311, USA

  • *Present address: Department of Nuclear Science, and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; cbertran@mit.edu
PDF

Phys. Rev. E 85, 031131 – Published 21 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.031131

Abstract

We investigate the connection between the theory of complete scaling and a field-theoretic (FT) treatment of asymmetric fluid criticality. To facilitate the comparison, we develop an equation of state from a simplified form of the complete scaling transformations and systematically compare this equation of state with the equation of state generated by a FT treatment of an asymmetric Landau-Ginzburg-Wilson Hamiltonian. We find, with care in interpretation, that these two approaches may be read as equivalent up to terms involving an independent higher-order asymmetric correction-to-scaling exponent.

View figure in article

Article Text

References (52)

  1. M. E. Fisher, in Critical Phenomena, edited by F. J. W. Hahne, Lecture Notes in Physics Vol. 186 (Springer, Berlin, 1982).
  2. C. Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor & Francis, London, 1996).
  3. J. V. Sengers and J. G. Shanks, J. Stat. Phys. 137, 857 (2009).
  4. T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952).
  5. M. A. Anisimov, E. E. Gorodetskii, V. D. Kulikov, and J. V. Sengers, Phys. Rev. E 51, 1199 (1995).
  6. I. Hahn, M. Weilert, F. Zhong, and M. Barmatz, J. Low Temp. Phys. 137, 579 (2004).
  7. L. Cailletet and E. C. Mathias, C. R. Hebd. Seances Acad. Sci. 102, 1202 (1886); 104, 1563 (1887).
  8. U. Närger and D. A. Balzarini, Phys. Rev. B 42, 6651 (1990).
  9. J. Weiner, K. H. Langley, and N. C. Ford Jr., Phys. Rev. Lett. 32, 879 (1974).
  10. B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970).
  11. N. D. Mermin, Phys. Rev. Lett. 26, 169 (1971).
  12. N. D. Mermin, Phys. Rev. Lett. 29, 957 (1971).
  13. J. J. Rehr and N. D. Mermin, Phys. Rev. A 8, 472 (1973).
  14. R. Guida and J. Zinn-Justin, J. Phys. A: Math. Gen. 31, 8103 (1998).
  15. J. F. Nicoll and R. K. P. Zia, Phys. Rev. B 23, 6157 (1981).
  16. J. F. Nicoll, Phys. Rev. A 24, 2203 (1981).
  17. C. Vause and J. Sak, Phys. Rev. A 21, 2099 (1980); 23, 1562(E) (1981).
  18. M. Ley-Koo and M. S. Green, Phys. Rev. A 23, 2650 (1981).
  19. F. C. Zhang and R. K. P. Zia, J. Phys. A: Math. Gen. 15, 3303 (1982).
  20. M. E. Fisher and G. Orkoulas, Phys. Rev. Lett. 85, 696 (2000).
  21. Y. C. Kim, M. E. Fisher, and G. Orkoulas, Phys. Rev. E 67, 061506 (2003).
  22. R. B. Griffiths and J. C. Wheeler, Phys. Rev. A 2, 1047 (1970).
  23. M. A. Anisimov and J. Wang, Phys. Rev. Lett. 97, 025703 (2006).
  24. J. Wang and M. A. Anisimov, Phys. Rev. E 75, 051107 (2007).
  25. C. E. Bertrand and M. A. Anisimov, Phys. Rev. Lett. 104, 205702 (2010).
  26. R. Ren, C. J. O'Keeffe, and G. Orkoulas, J. Chem. Phys. 125, 144505 (2006).
  27. C. N. Yang and C. P. Yang, Phys. Rev. Lett. 13, 303 (1964).
  28. G. Orkoulas, M. E. Fisher, and C. Üstün, J. Chem. Phys. 113, 7530 (2000).
  29. G. Orkoulas, M. E. Fisher, and A. Z. Panagiotopoulos, Phys. Rev. E 63, 051507 (2001).
  30. Y. C. Kim and M. E. Fisher, Chem. Phys. Lett. 414, 185 (2005).
  31. Y. C. Kim, M. E. Fisher, and E. Luijten, Phys. Rev. Lett. 91, 065701 (2003).
  32. Y. C. Kim and M. E. Fisher, Phys. Rev. E 68, 041506 (2003).
  33. Y. C. Kim, Phys. Rev. E 71, 051501 (2005).
  34. A. K. Wyczalkowska, M. A. Anisimov, J. V. Sengers, and Y. C. Kim, J. Chem. Phys. 116, 4202 (2002).
  35. C. A. Cerdeiriña, M. A. Anisimov, and J. V. Sengers, Chem. Phys. Lett. 424, 414 (2006).
  36. J. Wang, C. A. Cerdeiriña, M. A. Anisimov, and J. V. Sengers, Phys. Rev. E 77, 031127 (2008).
  37. G. Pérez-Sánchez, P. Losada-Pérez, C. A. Cerdeiriña, J. V. Sengers, and M. A. Anisimov, J. Chem. Phys. 132, 154502 (2010).
  38. M. Huang, Z. Chen, T. Yin, X. An, and W. Shen, J. Chem. Eng. Data 56, 2349 (2011).
  39. V. Vale, B. Rathke, S. Will, and W. Schröer, J. Chem. Eng. Data 56, 1330 (2011).
  40. S. C. Greer, B. K. Das, A. Kumar, and E. S. R. Gopal, J. Chem. Phys. 79, 4545 (1983).
  41. G. Pérez-Sánchez, P. Losada-Pérez, C. A. Cerdeiriña, and J. Thoen, J. Chem. Phys. 132, 214503 (2010).
  42. P. Losada-Pérez, C. S. P. Tripathi, J. Leys, C. A. Cerdeiriña, C. Glorieux, and J. Thoen, J. Chem. Phys. 134, 044505 (2011).
  43. M. E. Fisher and B. U. Felderhof, Ann. Phys. (NY) 58, 176 (1970); 58, 217 (1970).
  44. J. F. Nicoll and P. C. Albright, Phys. Rev. B 34, 1991 (1986).
  45. C. E. Bertrand, Ph.D. thesis, University of Maryland, 2011.
  46. R. B. Griffiths, Phys. Rev. 158, 176 (1967).
  47. P. Schofield, Phys. Rev. Lett. 22, 606 (1969).
  48. E. Brézin, D. J. Wallace, and K. G. Wilson, Phys. Rev. Lett. 29, 591 (1972).
  49. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6.
  50. F. J. Wegner, Phys. Rev. B 5, 4529 (1972).
  51. A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002).
  52. V. L. Kulinskii and N. P. Malomuzh, Phys. A (Amsterdam) 388, 621 (2009).

Outline

Information

Phys. Rev. E 85, 031131– Published 21 March, 2012
  • Received 9 February 2012
Article part of CHORUS

©2012 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation