arXiv subjects
Publications and source records attributed to D. P. Foster.
A square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, extended to include the effects of solvent quality, is examined in the framework of the Bethe approximation.
A recently introduced extension of the Corner Transfer Matrix Renormalisation Group (CTMRG) method useful for the study of self-avoiding walk type models is presented in detail and applied to a class of interacting self-avoiding walks due to Blöte and Nienhuis. This model displays two different types of collapse transition depending on model parameters. One is the standard $θ$-point transition. The other is found to give rise to a first-order collapse transition despite being known to be in other respects critical.
We present an extension of the corner transfer matrix renormalisation group (CTMRG) method to O(n) invariant models, with particular interest in the self-avoiding walk class of models (O(n=0)). The method is illustrated using an interacting self-avoiding walk model. Based on the efficiency and versatility when compared to other available numerical methods, we present CTMRG as the method of choice for two-dimensional self-avoiding walk problems.
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard $θ$-point model, the transition is first order. The phase diagram in the full fugacity-temperature plane displays an additional transition line, when compared to the $θ$-point model, as well as a critical transition at finite temperature in the hamiltonian walk limit.