Monte Carlo results for projected self-avoiding polygons: A two-dimensional model for knotted polymers

Journal of Physics A: Mathematical and General

Volumn 32, Issue 8, 1999, Pages 1359-1385

  Guitter, E ^a   Orlandini, E ^a  

^a CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033604974     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/8/006     Document Type: Article

References (27)

1. de Gennes P G 1972 Exponents for the excluded volume problem as derived by the Wilson method Phys. Lett. A 38 339-40
2. Sumners D W and Whittington S G 1988 Knots in self-avoiding walks J. Phys. A: Math. Gen. 21 1689-94
3. Pippenger N 1989 Knots in random walks Discr. Appl. Math. 25 273-8
4. Ribenkov V V, Cozzarelli N R and Vologodskii A V 1993 Probability of DNA knotting and the effective diameter of the DNA double helix Proc. Natl Acad. Sci., USA 90 5307-11
5. Shaw S Y and Wang J C 1993 Knotting of a DNA chain during ring closure Science 260 533-6
6. Janse van Rensburg E J and Whittington S G 1991 The dimensions of knotted polygons J. Phys. A: Math. Gen. 24 3935-48
7. Deguchi T and Tsurusaki K 1993 Topology of closed random polygons J. Phys. Soc. Japan 62 1411-14
8. Deguchi T and Tsurusaki K 1994 Statistical study of random knotting using Vasiliev invariants Random Knotting and Linking ed K C Millett and D W Sumners (Singapore: World Scientific) pp 89-121
9. Quake S 1994 Topological effects of knots in polymers Phys. Rev. Lett. 73 3317-20
10. Orlandini E, Tesi M C, Janse van Rensburg E J and Whittington S G 1996 Entropic exponents of lattice polygons with specified knot type J. Phys. A: Math. Gen. 29 L299-303
11. Orlandini E, Tesi M C, Janse van Rensburg E J and Whittington S G 1998 Asymptotics of knotted lattice polygons J. Phys. A: Math. Gen. 31 5953-67
12. For an introduction to knot theory see, for instance, Adams C C 1994 The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (New York: Freeman)
13. Berg B and Foester D 1981 Random paths and random surfaces on a digital computer Phys. Lett. B 106 323-6
14. Aragao de Carvalho C and Caracciolo S 1983 A new Monte Carlo approach to the critical properties of self-avoiding random walks J. Physique 44 323-31
15. 4-theory in four dimensions Nucl. Phys. B 215 209-48
16. Sokal A D and Thomas L E 1989 Exponential convergence to equilibrium for a class of random walk models J. Stat. Phys. 54 797-828
17. Caracciolo S, Pellissetto A and Sokal A D 1990 Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints J. Stat. Phys. 1-53
18. Geyer C J 1991 Markov chain Monte Carlo maximum likelihood Computing Science and Statistics: Proc. 23rd Symp. on the Interface ed E M Keramidas (Interface Foundation) pp 156-63
19. 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 J. Stat. Phys. 82 155-81
20. Orlandini E 1996 Monte Carlo study of polymer systems by Multiple Markov Chain method IMA Proc. Work p 7
21. Berretti A and Sokal A 1985 J. Stat. Phys. 40 1689-94
22. Caracciolo S, Pellissetto A and Sokal A D 1990 Monte Carlo test of hyperscaling relation for the two-dimensional self-avoiding walk: II J. Phys. A: Math. Gen. 23 4509-17
23. Nienhuis B 1982 Exact critical point and critical exponents of O(n) models in two dimensions Phys. Rev. Lett. 49 1062-5
24. Derrida B and De Seze L 1982 Application of the phenomenological renormalization to percolation and lattice animals in dimension 2 J. Physique 43 475-83
25. Janse van Rensburg E J and Madras N 1992 A non-local Monte Carlo algorithm for lattice trees J. Phys. A: Math. Gen. 25 303-33
26. Orlandini E, Seno F, Stella A L and Tesi M C 1992 Collapse from linear to branched polymer behaviour Phys. Rev. Lett. 68 488-91 See also Turban L 1983 Generalised self-avoiding walk J. Phys. A: Math. Gen. 16 L643-6
27. Orlandini E, Seno F, Stella A L and Tesi M C 1992 Collapse from linear to branched polymer behaviour Phys. Rev. Lett. 68 488-91 See also Turban L 1983 Generalised self-avoiding walk J. Phys. A: Math. Gen. 16 L643-6