Finite-size critical behavior in the Gibbs ensemble

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 3 SUPPL. A, 1997, Pages 2315-2320

  Bruce, A D ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

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EID: 0342316274     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.55.2315     Document Type: Article

References (33)

1. A.D. Bruce and N.B. Wilding, Phys. Rev. Lett. 68, 193 (1992); N.B. Wilding and A.D. Bruce, J. Phys. Condens. Matter 4, 3087 (1992).
2. A.D. Bruce and N.B. Wilding, Phys. Rev. Lett. 68, 193 (1992); N.B. Wilding and A.D. Bruce, J. Phys. Condens. Matter 4, 3087 (1992).
3. N.B. Wilding, Phys. Rev. E 52, 602 (1995).
4. A.Z. Panagiotopoulos, Mol. Phys. 61, 813 (1987); A.Z. Panagiotopoulos, N. Quirke, M. Stapeleton, and D.J. Tildesley, ibid. 63, 527 (1988).
5. A.Z. Panagiotopoulos, Mol. Phys. 61, 813 (1987); A.Z. Panagiotopoulos, N. Quirke, M. Stapeleton, and D.J. Tildesley, ibid. 63, 527 (1988).
6. For a review see A.Z. Panagiotopoulos, in Observation and Prediction of Phase Transitions in Complex Fluids, edited by M. Baus, R.F. Rull, and J.P. Ryckaert (Kluwer, Dordrecht, 1995), p. 463.
7. In the GE one needs only to ensure that the overall density lies somewhere in the range between those of the coexisting phases; this constraint sharpens with the approach to the critical point.
8. For a review of FSS, see Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).
9. B. Smit, Ph. de Smedt, and D. Frenkel, Mol. Phys. 68, 931 (1989).
10. A.Z. Panagiotopoulos, Int. J. Thermophys. 15, 1057 (1994).
11. K.K. Mon and K. Binder, J. Chem. Phys. 96, 6989 (1992).
12. K.K. Mon, Phys. Rev. B 47, 5497 (1993).
13. We make no notational distinction between the probability distributions of discrete variables and the probability densities of continuous variables.
14. See, e.g., T.L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).
15. See, e.g., A.M. Ferrenberg and R.H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988).
16. -2/(1+δ).
17. Some authors prefer to use the cumulant ratio U introduced by K. Binder, Z. Phys. B 43, 119 (1981); the relationship between the two cumulant ratios is G= -U/2.
18. D. Nicolaides and A.D. Bruce, J. Phys. A 21, 233 (1988); T.W. Burkhardt and B. Derrida, Phys. Rev. B 32, 7273 (1985).
19. D. Nicolaides and A.D. Bruce, J. Phys. A 21, 233 (1988); T.W. Burkhardt and B. Derrida, Phys. Rev. B 32, 7273 (1985).
20. A.D. Bruce, J. Phys. A 28, 3345 (1995); R. Hilfer, Z. Phys. B 96, 63 (1994); R. Hilfer and N.B. Wilding, J. Phys. A 28, L281 (1995).
21. A.D. Bruce, J. Phys. A 28, 3345 (1995); R. Hilfer, Z. Phys. B 96, 63 (1994); R. Hilfer and N.B. Wilding, J. Phys. A 28, L281 (1995).
22. A.D. Bruce, J. Phys. A 28, 3345 (1995); R. Hilfer, Z. Phys. B 96, 63 (1994); R. Hilfer and N.B. Wilding, J. Phys. A 28, L281 (1995).
23. G.R. Smith and A.D. Bruce, J. Phys. A 28, 6623 (1995).
24. V. Privman and M.E. Fisher, Phys. Rev. B 30, 322 (1984); see also Ref. [6].
25. 1→ 0 limits.
26. The note of reserve reflects the fact that the predictions for the full GE (i.e., the average over volumes) rest on the assumptions, detailed in the text, about the corrections featuring in Eq. (23).
27. C).
28. There are also some indications of structure of this kind in Fig. 5 of Ref. [4].
29. The peak observed does not have the sharpness of the cusp apparent in Figs. 1(b) and 2(b), but this is to be expected, since, as noted, the universal scaling form 11 will not describe the smallest systems visited in the simulations.
30. J.R. Recht and A.Z. Panagiotopoulos, Mol. Phys. 80, 843 (1993); D.G. Green, G. Jackson, E. de Miguel, and L.F. Rull, J. Chem. Phys. 101, 3190 (1994).
31. J.R. Recht and A.Z. Panagiotopoulos, Mol. Phys. 80, 843 (1993); D.G. Green, G. Jackson, E. de Miguel, and L.F. Rull, J. Chem. Phys. 101, 3190 (1994).
32. See also the discussion in Ref. [9],
33. And nonuniversal, in view of the remarks in [24].