Abstract
We investigate three simple lattice models of two dimensional vesicles. These models differ in their behavior from the universality class of partially convex polygons, which has been recently established. They do not have the tricritical scaling of those models, and furthermore display a surprising feature: their (perimeter) free energy is discontinuous with an isolated value at zero pressure. We give the full asymptotic descriptions of the generating functions in area and perimeter variables from theq-series solutions and obtain the scaling functions where applicable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. N. V. Temperly,Proc. Camb. Phil. Soc. 48:638 (1952).
L. Euler,Introductio in Analysis Infinitorum (Marcum-Michaelem Bousquet, Lausanne, 1748.
G. E. Andrews, inThe Theory of Partitions, G.-C. Rota, ed. (Addison-Wesley, Reading, Massachusetts, 1976).
M. Delest and G. Viennot,Theor. Comp. Sci. 34:169 (1984).
M. Delest,J. Math. Chem. 8:3 (1991).
V. Privman and N. M. Švrakić,Phys. Rev. Lett. 60:1107 (1988).
V. Privman and N. M. Švrakić,Directed Models of Polymers, Interfaces, and Clusters: Scaling and Finite-Size Properties, (Springer-Verlag, Berlin, 1989).
M. E. Fisher, A. J. Guttmann, and S. Whittington,J. Phys. A 24:3095 (1991).
R. Brak, A. L. Owczarek, and T. Prellberg,J. Stat. Phys. 76:1101 (1994).
T. Prellberg and R. Brak,J. Stat. Phys. 78:701 (1995).
M. Bousquet-Mélou, A method for the enumeration of various classes of column-convex polygons, University of Bordeaux Preprint (1993).
M. Bousquet-Mélou, The generating function of convex polyominoes: the resolution of aq-differential system, University of Bordeaux Preprint (1993).
t. Prellberg and A. L. Owczarek, Partially convex lattice vesicles: Methods and recent results,Int. J. Mod. Phys. B, to appear.
G. H. Hardy and S. Ramanujan,Proc. Lond. Math. Soc. (2)17:75 (1918).
F. C. Auluck,Proc. Camb. Phil. Soc. 47:679 (1951).
E. M. Wright,Q. J. Math. Oxford (2)19:313 (1968).
J. M. Fédou,Rep. Math. Phys. 34:57 (1994).
A. L. Owczarek and T. Prellberg,J. Stat. Phys. 70:1175 (1993).
T. Prellberg, Uniformq-series asymptotics for staircase polygons,J. Phys. A 28:1289 (1995).
G. H. Hardy,Divergent Series (Oxford University Press, Oxford, 1963).
G. H. Hardy,Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (Cambridge University Press, Cambridge, 1940).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prellberg, T., Owczarek, A.L. Stacking models of vesicles and compact clusters. J Stat Phys 80, 755–779 (1995). https://doi.org/10.1007/BF02178553
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02178553