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The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails,…
There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being…
A generalised model for interacting self-avoiding trails on the square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and…
In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the…
Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the…
The surface critical behaviour of the interacting self-avoiding trail is examined using transfer matrix methods coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points…
We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a…
We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained,…
Self-avoiding walks and self-avoiding trails, two models of a polymer coil in dilute solution, have been shown to be governed by the same universality class. On the other hand, self-avoiding walks interacting via nearest-neighbour contacts…
Self-avoiding walks self-interacting via nearest neighbours (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the polymer collapse transition of a polymer in dilute solution. On the square…
Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently, a two-dimensional model (triangular…
Results of a numerically exact transfer matrix calculation for the model of Interacting Self-Avoiding Trails are presented. The results lead to the conclusion that, at the collapse transition, Self-Avoiding Trails are in the same…
The study of the effect of random impurities on the collapse of a flexible polymer in dilute solution has had recent attention with consideration of semi-stiff interacting self-avoiding walks on the square lattice. In the absence of…
We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that…
We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight $\omega_l$ is assigned to each $(l+1)$-fold visited lattice site,…
We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…
We have simulated four-dimensional interacting self-avoiding trails (ISAT) on the hyper-cubic lattice with standard interactions at a wide range of temperatures up to length 4096 and at some temperatures up to length 16384. The results…
We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behaviour of this process is similar to the analogous process on the square…
The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using DMRG and coupled with finite-size scaling. Particular attention is paid to the critical…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…