N Madras et al 1990 J. Phys. A: Math. Gen. 23 5327 doi:10.1088/0305-4470/23/22/021
N Madras, C E Soteros, S G Whittington, J L Martin, M F Sykes, S Flesia and D S Gaunt
Show affiliationsThe authors consider a number of related lattice models of branched polymers in dilute solution in which the polymer is modelled as a tree or as an animal. In order to model the effect of the thermodynamic properties of changing the temperature, or the quality of the solvent, they consider counting cycles in animals and near-neighbour contacts in both animals and trees. They show that the free energies of these models have common features and derive rigorous upper and lower bounds on the temperature dependence of the free energies. Finally, they derive series data for several of these models and compare their estimates of the limiting free energy with the rigorous bounds.
65.20.-w Thermal properties of liquids
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
61.20.Gy Theory and models of liquid structure
61.25.H- Macromolecular and polymers solutions; polymer melts
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B30 Statistical thermodynamics (See also 80-XX)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 22 (21 November 1990)
N Madras et al 1990 J. Phys. A: Math. Gen. 23 5327
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