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Non-self-intersecting walks on the simple cubic and face-centered cubic lattices are used as a model for the linear polymer chain with excluded volume and nearest-neighbor interactions between the chain elements. The statistical properties of this model are investigated using the modified Monte Carlo technique for inversely restricted sampling. The following properties are investigated: the limiting distribution function of chain dimensions, the dependence of mean square length of the chain on the number of chain elements, and the thermodynamic properties of the chain. The results of these investigations are presented by a set of parametric representations. Each of these representations includes a parameter which is descriptive of long-range interactions in the polymer chain. These parameters are investigated for their dependence on the nearest-neighbor interaction parameter. A particular value for the nearest-neighbor interaction parameter is found, in which long-range interaction parameters reduce to the values they would attain were the chain simulated by an equivalent Markovian chain model. Thus, the conditions are found which uniquely define the Flory's theta point of the single chain. It is also found that an infinitely long single chain undergoes a phase transition which is associated with abrupt changes in the thermodynamic properties of the chain at a critical range of the nearest-neighbor interaction parameter.
Mazur et al. (Mon,) studied this question.