zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stacking models of vesicles and compact clusters. (English) Zbl 1106.82304
Summary: 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 the $q$-series solutions and obtain the scaling functions where applicable.

82B05Classical equilibrium statistical mechanics (general)
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Full Text: DOI
[1] H. N. V. Temperly,Proc. Camb. Phil. Soc. 48:638 (1952).
[2] L. Euler,Introductio in Analysis Infinitorum (Marcum-Michaelem Bousquet, Lausanne, 1748.
[3] G. E. Andrews, inThe Theory of Partitions, G.-C. Rota, ed. (Addison-Wesley, Reading, Massachusetts, 1976).
[4] M. Delest and G. Viennot,Theor. Comp. Sci. 34:169 (1984). · doi:10.1016/0304-3975(84)90116-6
[5] M. Delest,J. Math. Chem. 8:3 (1991). · doi:10.1007/BF01166920
[6] V. Privman and N. M. Švrakić,Phys. Rev. Lett. 60:1107 (1988). · doi:10.1103/PhysRevLett.60.1107
[7] V. Privman and N. M. Švrakić,Directed Models of Polymers, Interfaces, and Clusters: Scaling and Finite-Size Properties, (Springer-Verlag, Berlin, 1989).
[8] M. E. Fisher, A. J. Guttmann, and S. Whittington,J. Phys. A 24:3095 (1991). · doi:10.1088/0305-4470/24/13/023
[9] R. Brak, A. L. Owczarek, and T. Prellberg,J. Stat. Phys. 76:1101 (1994). · Zbl 0839.60099 · doi:10.1007/BF02187057
[10] T. Prellberg and R. Brak,J. Stat. Phys. 78:701 (1995). · Zbl 1102.82316 · doi:10.1007/BF02183685
[11] M. Bousquet-Mélou, A method for the enumeration of various classes of column-convex polygons, University of Bordeaux Preprint (1993). · Zbl 0793.05003
[12] M. Bousquet-Mélou, The generating function of convex polyominoes: the resolution of aq-differential system, University of Bordeaux Preprint (1993). · Zbl 0793.05003
[13] t. Prellberg and A. L. Owczarek, Partially convex lattice vesicles: Methods and recent results,Int. J. Mod. Phys. B, to appear. · Zbl 1049.82515
[14] G. H. Hardy and S. Ramanujan,Proc. Lond. Math. Soc. (2)17:75 (1918). · doi:10.1112/plms/s2-17.1.75
[15] F. C. Auluck,Proc. Camb. Phil. Soc. 47:679 (1951). · doi:10.1017/S0305004100027134
[16] E. M. Wright,Q. J. Math. Oxford (2)19:313 (1968). · Zbl 0253.05007 · doi:10.1093/qmath/19.1.313
[17] J. M. Fédou,Rep. Math. Phys. 34:57 (1994). · Zbl 0806.33014 · doi:10.1016/0034-4877(94)90017-5
[18] A. L. Owczarek and T. Prellberg,J. Stat. Phys. 70:1175 (1993). · Zbl 1081.82542 · doi:10.1007/BF01049427
[19] T. Prellberg, Uniformq-series asymptotics for staircase polygons,J. Phys. A 28:1289 (1995). · Zbl 0852.33011 · doi:10.1088/0305-4470/28/5/016
[20] G. H. Hardy,Divergent Series (Oxford University Press, Oxford, 1963). · Zbl 0897.01044
[21] G. H. Hardy,Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (Cambridge University Press, Cambridge, 1940). · Zbl 0025.10505