D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853-856. Home/Search Document Not in Database Summary APS Related Articles Check |
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New Enumerative Results on Two-Dimensional Directed Animals - Bousquet-Mélou (1998) (1 citation) (Correct)
....are given in Figure 2. The edges are oriented upwards in all lattices. The leftmost animal has area 12 and perimeter 10. O O O (b) c) a) Figure 2: Directed animals on two dimensional lattices. Directed animals are related to directed (site) percolation models. Moreover, as shown by Dhar [12], enumerating directed animals according to the area on certain graphs is equivalent to solving a hard particle model on another graph. For instance, directed animals on the square lattice correspond to a simple hard particle model in one dimension, but animals on the honeycomb lattice do not ....
....the area, for the few exact known results in this domain can be obtained by solving the corresponding gas model. The main two results are the area generating functions for directed animals on the square lattice and on the threedimensional next nearest neighbour cubic lattice drawn in Figure 4(a) [11, 12]. For square lattice animals, there exists, besides the gas model argument, a very simple and nice combinatorial proof based on the notion of heaps of pieces [3, 4, 22] However, this combinatorial method has not (yet) been extended to animals in three dimensions, for which the very difficult ....
[Article contains additional citation context not shown here]
D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853--856.
Enumeration of Directed Animals on an Infinite Family of.. - Bousquet-Mélou, Conway (1996) (Correct)
....are known. In 1982, Dhar, Phani and Barma gave two conjectures on the number of directed animals on the square and triangular lattices [1] These conjectures can be restated in the form of quadratic expressions for the corresponding generating functions, and were then proved in several ways [2, 3, 4, 5, 6]. Dhar [6] also solved the enumeration problem on a three dimensional lattice through a correspondence with the hard hexagon model solved by Baxter [7] The associated area generating function is again algebraic, but of degree 12 [8] Directed animals on other lattices have been enumerated by ....
.... Dhar, Phani and Barma gave two conjectures on the number of directed animals on the square and triangular lattices [1] These conjectures can be restated in the form of quadratic expressions for the corresponding generating functions, and were then proved in several ways [2, 3, 4, 5, 6] Dhar [6] also solved the enumeration problem on a three dimensional lattice through a correspondence with the hard hexagon model solved by Baxter [7] The associated area generating function is again algebraic, but of degree 12 [8] Directed animals on other lattices have been enumerated by computer with ....
[Article contains additional citation context not shown here]
D. Dhar. Exact solution of a directed-site animals-enumeration problem in three dimensions. Phys. Rev. Lett., 51:853--856, 1983.
Enumeration of Three-Dimensional Convex Polygons - Bousquet-Mélou, Guttmann (Correct)
....combinatorial interpretation of the form of the solution. Our three dimensional result is new and extends the (short) list of exactly solved 3 dimensional models: in this connection, let us cite the Zamolodchikov model [1] directed animals on the cubic lattice with next nearest neighbour bonds [8], and a variety of results on plane partitions, starting with MacMahon [27] Our method is new, that is, is not an extension of any of the methods previously used to count convex SAP on the square lattice. It underlines the fact that counting convex SAP on ZZ is, essentially, a 1 dimensional ....
D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853--856.
Branched Polymers and Dimensional Reduction - Brydges, Imbrie (2001) (Correct)
....in this paper. This is not the case for z c . In 1981 Parisi and Sourlas [PS81] conjectured exact values of and other critical exponents for self avoiding branched polymers in D 2 dimensions by relating them to the Yang Lee singularity of an Ising model in D dimensions. Various authors [Dha83, LF95, PF99] have also argued that the exponents of the Yang Lee singularity are related in exact and simple ways to exponents for the hard core gas at the negative value of activity which is the closest singularity to the origin in the pressure. In this paper we consider these models in the continuum and ....
....and the Yang Lee edge, leaves little room to doubt the result of Parisi and Sourlas. The universal repulsive core singularity and the Yang Lee edge. This connection goes back to two articles: Cardy [Car82] related the YangLee edge in D dimensions to directed animals in D 1 dimensions, and Dhar [Dha83] related directed animals in D 1 dimensions to hard core lattice gases in D dimensions. Dhar (and later Baram and Luban [BL87] also used Baxter s solution [Bax82] to the hard hexagon model in D = 2 (continued to negative activity) to determine the free energy exponent (2) 6 . Hence (2) ....
[Article contains additional citation context not shown here]
D. Dhar. Exact solution of a directed-site animals-enumeration problem. Phys. Rev. Lett., 51:853-856, 1983.
Enumeration of Three-Dimensional Convex Polygons - Bousquet-Mélou, Guttmann (1997) (Correct)
....combinatorial interpretation of the form of the solution. Our three dimensional result is new and extends the (short) list of exactly solved 3 dimensional models: in this connection, let us cite the Zamolodchikov model [1] directed animals on the cubic lattice with next nearest neighbour bonds [8], and a variety of results on plane partitions, starting with MacMahon [27] Our method is new, that is, is not an extension of any of the methods previously used to count convex SAP on the square lattice. It underlines the fact that counting convex SAP on ZZ d is, essentially, a 1 dimensional ....
D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853--856.
Enumeration of Directed Animals on an Infinite Family of .. - Bousquet-Mélou.. (1996) (Correct)
....are known. In 1982, Dhar, Phani and Barma gave two conjectures on the number of directed animals on the square and triangular lattices [1] These conjectures can be restated in the form of quadratic expressions for the corresponding generating functions, and were then proved in several ways [2, 3, 4, 5, 6]. Dhar [6] also solved the enumeration problem on a three dimensional lattice through a correspondence with the hard hexagon model solved by Baxter [7] The associated area generating function is again algebraic, but of degree 12 [8] Directed animals on other lattices have been enumerated by ....
.... Dhar, Phani and Barma gave two conjectures on the number of directed animals on the square and triangular lattices [1] These conjectures can be restated in the form of quadratic expressions for the corresponding generating functions, and were then proved in several ways [2, 3, 4, 5, 6] Dhar [6] also solved the enumeration problem on a three dimensional lattice through a correspondence with the hard hexagon model solved by Baxter [7] The associated area generating function is again algebraic, but of degree 12 [8] Directed animals on other lattices have been enumerated by computer with ....
[Article contains additional citation context not shown here]
D. Dhar. Exact solution of a directed-site animals-enumeration problem in three dimensions. Phys. Rev. Lett., 51:853--856, 1983.
New Enumerative Results on Two-Dimensional Directed Animals - Bousquet-Mélou (1998) (1 citation) (Correct)
....lattices. Examples are given in Figure 2. The edges are oriented upwards in all lattices. The leftmost animal has area 12 and perimeter 10. O O O Figure 2: Directed animals on two dimensional lattices. Directed animals are related to directed (site) percolation models. Moreover, as shown by Dhar [11], enumerating directed animals according to area on certain graphs is equivalent to solving a hard particle gas model on other graphs. A hard particle gas model is a statistical lattice model in which two adjacent vertices cannot be simultaneously occupied by molecules of gas. A combinatorial ....
....them according to the area: the few exact known results can be obtained by solving the corresponding gas model. The main two results are the area generating functions of directed animals on the square lattice and on the threedimensional next nearest neighbour lattice drawn in Figure 3(a) [11]. For square lattice animals, there exists, besides the gas model argument, a very simple and nice combinatorial proof based on the notion of heaps of pieces [4, 15] However, this combinatorial method has not (yet) been extended to animals in three dimensions, for which the very difficult ....
[Article contains additional citation context not shown here]
D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853--855.
New Enumerative Results on Two-Dimensional Directed Animals - Bousquet-Mélou (1998) (1 citation) (Correct)
....are given in Figure 2. The edges are oriented upwards in all lattices. The leftmost animal has area 12 and perimeter 10. O O O (b) c) a) Figure 2: Directed animals on two dimensional lattices. Directed animals are related to directed (site) percolation models. Moreover, as shown by Dhar [12], enumerating directed animals according to the area on certain graphs is equivalent to solving a hard particle model on another graph. For instance, directed animals on the square lattice correspond to a simple hard particle model in one dimension, but animals on the honeycomb lattice do not ....
....the area, for the few exact known results in this domain can be obtained by solving the corresponding gas model. The main two results are the area generating functions for directed animals on the square lattice and on the threedimensional next nearest neighbour cubic lattice drawn in Figure 4(a) [11, 12]. For square lattice animals, there exists, besides the gas model argument, a very simple and nice combinatorial proof based on the notion of heaps of pieces [3, 4, 22] However, this combinatorial method has not (yet) been extended to animals in three dimensions, for which the very difficult ....
[Article contains additional citation context not shown here]
D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853--856.
Lattice Animals and Heaps of Dimers - Bousquet-Melou, Rechnitzer (Correct)
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D. Dhar, Exact solution of a directed-site animals-enumeration problem in three dimensions, Phys. Rev. Lett. 51 (1983) 853-856.
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