Lubensky, T. C. ; Dasgupta, C. ; Chaves, C. M.
(1978)
*Statistics of trees and branched polymers from a generalised Hilhorst model
*
Journal of Physics A: Mathematical and General, 11
(11).
pp. 2219-2236.
ISSN 0305-4470

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Official URL: http://iopscience.iop.org/0305-4470/11/11/010

Related URL: http://dx.doi.org/10.1088/0305-4470/11/11/010

## Abstract

A generalisation of the Hilhorst model in which at each site, x, on a lattice, there is an n-state variable nu (x), and an s-state variable, sigma (x), which interact via a Hamiltonian H=-nK Sigma _{(x,x')} delta ^{nu (x) nu (x')}(s delta ^{sigma (x) sigma (x')}-1)-h Sigma _{x} delta ^{nu (x)}^{1}-1) is introduced. It is shown that if (s-1)= lambda n, the n=0 limit of the partition function for this model is the generating function for trees in which ln K is the chemical potential for bonds (monomers), ln lambda for the number of trees (polymers) an ln h for the number of free ends of all trees. Fields which mark any point and fields which mark only external points of a polymer are identified. The above Hamiltonian is converted to a field theory which is used to discuss the dependence on the monomer number, N, of critical properties such as the radius of gyration of branched polymers with a small number of branchings. It is shown that these properties are controlled by the usual n=0 polymer fixed point.

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ID Code: | 83436 |

Deposited On: | 20 Feb 2012 12:15 |

Last Modified: | 20 Feb 2012 12:15 |

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