D Bennett-Wood et al 1995 J. Phys. A: Math. Gen. 28 5143 doi:10.1088/0305-4470/28/18/007
D Bennett-Wood, J L Cardy, S Flesia, A J Guttmann and A L Owczarek
Show affiliationsWe consider oriented self-avoiding walks on the square lattice with different energies between steps that are oriented parallel or antiparallel across a face of the lattice. Rigorous bounds on the free energy and exact enumeration data are used to study the statistical mechanics of this model. We conjecture a phase diagram in the parallel-antiparallel interaction plane, and discuss the order of the associated phase transitions. The question, raised by previous field theoretical considerations, of the existence of an exponent that varies continuously with the energy of interaction is discussed at length. In connection with this we have also studied two oriented walks fixed at a common origin; this being the simplest model of branched oriented polymers in two dimensions. The evidence, although not conclusive, tends to support the field theoretic prediction.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 18 (21 September 1995)
D Bennett-Wood et al 1995 J. Phys. A: Math. Gen. 28 5143
J H Booske et al 1986 Plasma Phys. Control. Fusion 28 1449
J Bordas et al 1978 J. Phys. C: Solid State Phys. 11 2607
Zhongtian Wang 1999 Plasma Phys. Control. Fusion 41 A679