Counting lattice animals in high dimensions

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 9, 2011, Pages

  Luther, Sebastian ^a   Mertens, Stephan ^a,b  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b SANTA FE INSTITUTE   (United States)

Author keywords

critical exponents and amplitudes (theory); disordered systems (theory); percolation problems (theory)

Indexed keywords

EID: 80053524051     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/09/P09026     Document Type: Article

References (29)

1. Golomb S W 1994 Polyominoes 2nd edn (Princeton, NJ: Princeton University Press)
2. Stauffer D and Aharony A 1992 Introduction to Percolation Theory 2nd edn (London: Taylor and Francis)
3. Guttmann A J (ed) 2009 Polygons, Polyominoes and Polycubes (Springer Lecture Notes in Physics vol 775) (Heidelberg: Springer)
4. Klarner D A 1967 Cell growth problems Can. J. Math. 19 851
5. Madras N 1999 A pattern theorem for lattice clusters Ann. Comb. 3 357
6. Barequet R, Barequet G and Rote G 2010 Formulae and growth rates of high-dimensional polycubes Combinatorica 30 257
7. Redelmeier D H 1981 Counting polyominoes: yet another attack Discrete Math. 36 191
8. Mertens S 1990 Lattice animals: a fast enumeration algorithm and new perimeter polynomials J. Stat. Phys. 58 1095
9. Mertens S and Lautenbacher M E 1992 Counting lattice animals: a parallel attack J. Stat. Phys. 66 669
10. Jensen I 2001 Enumerations of lattice animals and trees J. Stat. Phys. 102 865
11. Aleksandrowicz G and Barequet G 2009 Counting d-dimensional polycubes and nonrectangular planar polyominoes Int. J. Comput. Geometry Appl. 19 215
12. Aleksandrowicz G and Barequet G 2009 Counting polycubes without the dimensionality curse Discrete Math. 309 4576
13. Conway J H and Sloane N J A 1997 Low-dimensional lattices. VII coordination sequences Proc. R. Soc. A 453 2369
14. Gaunt D S, Sykes M F and Ruskin H 1976 Percolation processes in d-dimensions J. Phys. A: Math. Gen. 9 1899
15. Mertens S 2011 Lattice animals www.ovgu.de/mertens/research/animals
16. Gaunt D S 1980 The critical dimension for lattice animals J. Phys. A: Math. Gen. 13 L97
17. Lunnon W F 1975 Counting multidimensional polyominoes Comput. J. 18 366
18. Cayley A 1889 A theorem on trees Q. J. Pure Appl. Math. 23 376
19. Cameron P J 1995 Counting two-graphs related to trees Electron. J. Comb. 2 R4
20. Fisher M E and Essam J W 1961 Some cluster size and percolation problems J. Math. Phys. 2 609
21. Peard P J and Gaunt D S 1995 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer J. Phys. A: Math. Gen. 28 6109
22. Adler J, Meir Y, Harris A B, Aharony A and Duarte J A M S 1988 Series study of random animals in general dimensions Phys. Rev. B 38 4941
23. Parisi G and Sourlas N 1981 Critical behavior of branched polymers and the Lee-Yang edge singularity Phys. Rev. Lett. 46 871
24. Imbrie J Z 2003 Dimensional reduction and crossover to mean-field behavior for branched polymers Annal. Henri Poincaré 4 S445
25. Dhar D 1983 Exact solution of a directed-site animals-enumeration problem in three dimensions Phys. Rev. Lett. 51 853
26. Lubensky T C and Isaacson Joel 1979 Statistics of lattice animals and dilute branched polymers Phys. Rev. A 20 2130
27. Hsu H-P, Nadler W and Grassberger P 2005 Simulations of lattice animals and trees J. Phys. A: Math. Gen. 38 775
28. Hsu H-P, Nadler W and Grassberger P 2005 Statistics of lattice animals Comput. Phys. Commun. 169 114
29. Gaunt D S and Peard P J 2000 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers J. Phys. A: Math. Gen. 33 7515