Scaling behaviour of two-dimensional polygon models

Journal of Statistical Physics

Volumn 108, Issue 3-4, 2002, Pages 459-493

  Richard, Christoph ^a,b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

Exact solution; Scaling; Self avoiding polygons; Vesicles

Indexed keywords

EID: 0036095316     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015773723188     Document Type: Article

References (32)

1. C. Vanderzande, Lattice Models of Polymers (Cambridge University Press, Cambridge, 1998).
2. E. J. Janse van Rensburg, The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles (Oxford University Press, New York, 2000).
3. S. Leibler, R. R. P. Singh, and M. E. Fisher, Thermodynamic behaviour of two-dimensional vesicles, Phys. Rev. Lett. 59:1989-1992 (1987).
4. M. E. Fisher, Fractal and nonfractal shapes in two-dimensional vesicles, Physica D 38:112-118 (1989).
5. M. E. Fisher, A. J. Guttmann and S. G. Whittington, Two-dimensional lattice vesicles and polygons, J. Phys. A 24:3095-3106 (1991).
6. J. L. Cardy and A. J. Guttmann, Universal amplitude combinations for self-avoiding walks, polygons and trails, J. Phys. A 26:2485-2494 (1993).
7. J. L. Cardy, Mean area of self-avoiding loops, Phys. Rev. Lett. 72:1580-1583 (1994).
8. I. Jensen and A. J. Guttmann, Self-avoiding polygons on the square lattice, J. Phys. A 32:4867-4876 (1999).
9. I. Jensen, Size and area of square lattice polygons, J. Phys. A 32:3533-3543 (2000).
10. C. Richard, A. J. Guttmann, and I. Jensen, Scaling function and universal amplitude combinations for self-avoiding polygons, J. Phys. A 34:L495-L501 (2001).
11. J. L. Cardy, Exact scaling functions for self-avoiding loops and branched polymers, J. Phys. A 34:L665-L672 (2001).
12. T. Prellberg and R. Owczarek, Partially convex lattice vesicles: Methods and recent results, Proc. Conf. on Confronting the Infinite (World Scientific, Singapore, 1995), pp. 204-214.
13. M. Bousquet-Mélou, A method for the enumeration of various classes of column-convex polygons, Discr. Math. 154:1-25 (1996).
14. R. Brak and A. J. Guttmann, Exact solution of the staircase and row-convex polygon perimeter and area generating function, J. Phys. A 23:4581-4588 (1990).
15. K. Y. Lin, Exact solution of the convex polygon perimeter and area generating function, J. Phys. A 24:2411-2417 (1991).
16. M. Bousquet-Mélou, Convex polyominoes and algebraic languages, J. Phys. A 25:1935-1944 (1992).
17. R. Brak, A. L. Owczarek, and T. Prellberg, Exact scaling behaviour of partially convex vesicles, J. Stat. Phys. 76:1101-1128 (1994).
18. T. Prellberg and R. Brak, Critical exponents from nonlinear functional equations for partially directed cluster models, J. Stat. Phys. 78:701-730 (1995).
19. A. D. Rechnitzer, Some Problems in the Counting of Lattice Animals, Polyominoes, Polygons and Walks, Ph.D. Thesis (The University of Melbourne, 2000).
20. R. P. Stanley, Differentiably finite power series, Eur. J. Comb. 1:175-188 (1980).
21. A. R. Conway, A. J. Guttmann, and M. Delest, The number of three-choice polygons, Math. Comp. Modelling 26:51-58 (1997).
22. T. Prellberg and R. Owczarek, Stacking models of vesicles and compact clusters, J. Stat. Phys. 80:755-779 (1995).
23. T. Prellberg, Uniform q-series asymptotics for staircase polygons, J. Phys. A 28:1289-1304 (1995).
24. A. L. Owczarek, J. W. Essam, and R. Brak, Scaling analysis for the adsorption transition in a watermelon network of n directed non-intersecting walks, J. Stat. Phys. 102:997-1017 (2001).
25. C. Richard and A. J. Guttmann, q-Linear approximants: Scaling functions for polygon models, J. Phys. A 34:4783-4796 (2001).
26. E. Hille, Analytic Function Theory (Waltham, Blaisdell, Massachusetts, 1959).
27. A. L. Owczarek, T. Prellberg, and R. Brak, The tricritical behaviour of self-interacting partially directed walks, J. Stat. Phys. 72:737-772 (1993).
28. R. Brak and A. J. Guttmann, Algebraic approximants: A new method of series analysis, J. Phys. A 23: L1331-L1337 (1990).
29. A. R. Conway and A. J. Guttmann, Square lattice self-avoiding walks and corrections to scaling, Phys. Rev. Lett. 77:5284-5287 (1996).
30. D. F. Styer, Subroutine library for partial differential approximants, Comput. Phys. Commun. 61:374-386, (1990).
31. T. Prellberg and A. L. Owczarek, On the asymptotics of the finite-perimeter partition function of two-dimensional lattice vesicles, Commun. Math. Phys. 201:493-505 (1999).
32. R. Brak, A. L. Owczarek, and T. Prellberg, A scaling theory of the collapse transition in geometric cluster models of polymers and vesicles, J. Phys. A 26:4565-4579 (1993).