Multiple Markov chain Monte Carlo study of adsorbing self-avoiding walks in two and in three dimensions

Journal of Physics A: Mathematical and General

Volumn 37, Issue 27, 2004, Pages 6875-6898

  Van Rensburg, E J Janse ^a   Rechnltzer, A R ^b  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142545789     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/27/002     Document Type: Article

References (41)

1. Batchelor M T and Yung C M 1995 Exact results for the adsorption of a flexible self-avoiding polymer chain in two dimensions Phys. Rev. Lett. 74 2026-9
2. Berretti A and Sokal A D 1985 New Monte Carlo method for walk J. Stat. Phys. 40 483-531
3. Burkhardt T W, Eisenriegler E and Guim I 1989 Conformal theory of energy correlations in the semi-infinite two dimensional 0(n) model Nucl. Phys. B 316 559-72
4. Caracciolo S, Causo M S and Pelisetto A 1998 High precision determination of the critical exponent γ for self-avoiding walks Phys. Rev. E 57 R1215-8
5. de Gennes P-G 1975 Collapse of a polymer chain in poor solvents J. Physique 36 L55-7
6. de Gennes P-G 1976 Scaling theory of polymer adsorption J. Physique 37 1445-52
7. de Gennes P-G 1979 Scaling Concepts in Polymer Physics (Ithaca, NY: Cornell University Press)
8. Eisenriegler E, Kremer K and Binder K 1982 J. Chem. Phys. 77 6296-304
9. Geyer C J and Thompson E A 1994 University of Minnesota Preprint
10. Guttmann A J and Conway A R 2001 Square lattice self-avoiding walks and polygons Ann. Comb. 5 319-45
11. Flory P J 1955 Statistical thermodynamics of semi-flexible chain molecules Proc. R. Soc. Lond. A 234 60-73
12. Flory P J 1969 Statistical Mechanics of Chain Molecules (New York: Wiley Interscience)
13. Hammersley J M 1957 Percolation processes: II. The connective constant Math. Proc. Camb. Phil. Soc. 53 642-5
14. Hammersley J M and Handscomb D C 1964 Monte Carlo Methods (London: Chapman and Hall)
15. Hammersley J M, Torrie G M and Whittington S G 1982 Self-avoiding walks interacting with a surface J. Phys. A: Math. Gen. 15 539-71
16. Hara T and Slade G 1990 The lace expansion for self-avoiding walk in five or more dimensions Rev. Math. Phys. 4 235-327
17. Hegger R and Grassberger P 1994 Chain polymers near an adsorbing surface J. Phys. A: Math. Gen. 27 4069-81
18. Janse van Rensburg E J 1998 Collapsing and adsorbing polygons J. Phys. A: Math. Gen. 31 8295-306
19. Jensen I and Guttmann A J 1998 Self-avoiding walks, neighbour-avoiding walks and trials on semi-regular lattices J. Phys. A: Math. Gen. 31 8137-45
20. Jensen I and Guttmann A J 1999 Self-avoiding polygons on the square lattice J. Phys. A: Math. Gen. 32 4867-76
21. Kesten H 1963 On the number of self-avoiding walks J. Math. Phys. 4 960-9
22. Kesten H 1964 On the number of self-avoiding walks J. Math. Phys. 5 1128-37
23. Lawrie I D and Saribach S 1984 Tricriticality Phase Transitions and Critical Phenomena vol 9, ed C Domb and J L Lebowitz (New York: Academic) pp 65-161
24. Li B, Madras N and Sokal A D 1995 Critical exponents, hyperscaling, and universal amplitude ratios for two and three dimensional self-avoiding walks J. Stat. Phys. 80 661-754
25. MacDonald D, Joseph S, Hunter D L, Moseley L L, Jan N and Guttmann A J 2000 Self-avoiding walks on the simple cubic lattice J. Phys. A: Math. Gen. 33 5973-83
26. Madras N 1988 End patterns of self-avoiding walks J. Stat. Phys. 53 689-701
27. Madras N 1999 A pattern theorem for lattice clusters Ann. Comb. 3 357-84
28. Madras N and Slade G 1993 The Self-Avoiding Walk (Cambridge, MA: Birkhäuser Boston)
29. Madras N and Sokal A D 1988 The pivot algorithm: a highly efficient Monte Carlo method for the self-avoiding walk J. Stat. Phys. 50 109-86
30. Meirovitch H and Chang I 1993 Surface critical exponents of self-avoiding walks on a square lattice with an adsorbing boundary Phys. Rev. E 48 1960-9
31. Meirovitch H and Livne S 1988 Computer simulation of long polymers adsorbed on a surface: II. Critical behaviour of a single self-avoiding walk J. Chem. Phys. 88 4507-15
32. Nienhuis B 1987 Phase Transitions and Critical Phenonema vol 11, ed C Domb and J L Lebowitz (New York: Academic)
33. Owczarek A L, Prellberg T and Brak R 1993 New scaling form for the collapsed polymer phase Phys. Rev. Lett. 70 951-3
34. Prellberg T and Krawczyk J 2004 Flat histogram PERM Phys. Rev. Lett. 92 120602
35. Rechnitzer A and Janse van Rensburg E J 2002 Canonical Monte Carlo determination of the connective constant of self-avoiding walks J. Phys. A: Math. Gen. 35 L605-12
36. Tesi M C, Janse van Rensburg E J, Orlandini E and Whittington S G 1996 Monte Carlo study of the interacting self-avoiding walk model in three dimensions J. Stat. Phys. 82 155-81
37. Vrbová T and Procházka K 1999 Adsorption of self-avoiding walks at an impenetrable plane in the expanded phase: a Monte Carlo study J. Phys. A: Math. Gen. 32 5469-75
38. Vrbová T and Whittington S G 1996 Adsorption and collapse of self-avoiding walks and polygons in three dimensions J. Phys. A: Math. Gen. 29 6253-64
39. Vrbová T and Whittington S G 1998 Adsorption and collapse of self-avoiding walks at a defect plane J. Phys. A: Math. Gen. 31 7031-41
40. Vrbová T and Whittington S G 1998 Adsorption and collapse of self-avoiding walks in three dimensions: a Monte Carlo study J. Phys. A: Math. Gen. 313989-98
41. You S and Janse van Rensburg E J 2001 Adsorbing trees in two dimensions: a Monte Carlo study Phys. Rev. E 64 046101-2-9