Model Of Self-avoiding Trails Research Articles

Polymer collapse of a self-avoiding trail model on a two-dimensional inhomogeneous lattice

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 impurities the model displays two types of collapsed phase, one of which is both anisotropically ordered and maximally dense (crystal-like). In the presence of impurities the study showed that the crystal type phase disappears. Here we investigate extended interacting self-avoiding trails on the triangular lattice with random impurities. Without impurities this model also displays two collapsed phases, one of which is maximally dense but not ordered anisotropically and so may be affected differently by a disorderd lattice. The trails are simulated using the flatPERM algorithm and the inhomogeneity is realised by making a random fraction of the lattice unavailable to the trails. We calculate several thermodynamic and metric quantities to map out the phase diagram and look at how the amount of disorder affects the properties of each phase but especially the maximally dense phase. Our results indicate that while the maximally dense phase in the trail model is affected less than in the walk model it is also disrupted and becomes a denser version of the globule phase so that the model with impurities displays no more than one true thermodynamic collapsed phase.

Self-Avoiding Trail model in two-dimensional regular lattices: Study of conformational quantities and relation with the Self-Avoiding Walk model

The Self-Avoiding Trail (SAT) is a random walk model represented by an N-step lattice path, with forbidden step overlaps. The SAT is a variant of the Self-Avoiding Walk (SAW) model, where a site is visited only once. There is a consensus that SAT is in the same universality class of SAW, implying that the scaling behavior of conformational quantities, represented by the exponents ν0 and Δ1, is the same in both models. However, in comparison to SAW, SAT results exhibit most pronounced finite-size effects and inconsistent estimates of ν0, depending on the lattice coordination number and conformational quantity. The scaling behavior of the persistence length, λN, is in disagreement with recent estimates for the SAW model. Also, the influence of coordination number on the lattice-dependent constants requires a better understanding. In this study, we revisit the SAT model with data generated by the pivot algorithm up to N=8000 steps, for the hexagonal, square and triangular lattices. Accordingly, we find compelling evidences that ν0 and Δ1 values are the same for the SAT and SAW models, regardless the lattice and conformational quantity used, while the most pronounced finite-size effect comes from the higher amplitude of the correction to scaling terms. Similarly to SAW, we find the λN convergence to lattice dependent constant λ∞(SAW) for the SAT model. Based on the ratio λ∞(SAW)/λ∞(SAT)∝z/2, where z is the lattice coordination number, we find that the factor z/2 quantifies the relation between SAW and SAT lattice dependent constants.

Self-Avoiding Trail Model in Two-Dimensional Regular Lattices: Study of Conformational Quantities and Relation with the Self-Avoiding Walk Model

Self-Avoiding Trail Model in Two-Dimensional Regular Lattices: Study of Conformational Quantities and Relation with the Self-Avoiding Walk Model

Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model.

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, and , are estimated from the scaling behavior of the leading partition function zeros.

Lattice polymers with two competing collapse interactions

We study a generalized model of self-avoiding trails, containing two different types of interaction (nearest-neighbour contacts and multiply visited sites), using computer simulations. This model contains various previously studied models as special cases. We find that the strong collapse transition induced by multiply-visited sites is a singular point in the phase diagram and corresponds to a higher order multi-critical point separating a line of weak second-order transitions from a line of first-order transitions.

Weighting of topologically different interactions in a model of two-dimensional polymer collapse

We study by computer simulation a recently introduced generalized model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely, crossings where the trail passes across itself and collisions where the lattice path visits the same site without crossing. This model generalizes the canonical interacting self-avoiding trail model of polymer collapse, which has a strongly divergent specific heat at its transition point. We confirm the recent prediction that the asymmetry does not affect the universality class for a range of asymmetry. Certainly, where the weighting of collisions outweighs that of crossings this is well supported numerically. When crossings are weighted heavily relative to collisions, the collapse transition reverts to the canonical θ-point-like behavior found in interacting self-avoiding walks.

Generalized interacting self-avoiding trails on the square lattice: Phase diagram and critical behavior

A generalized model for interacting self-avoiding trails on a square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and crossings. Rigidity is also included in the model. The model includes the Nienhuis O(n=0) model and the interacting self-avoiding trail model as special cases. It is shown that the generic type of collapse found is the same as in the pure interacting self-avoiding trail model.

Identification of a polymer growth process with an equilibrium multicritical collapse phase transition: The meeting point of swollen, collapsed, and crystalline polymers

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the θ point of the interacting self-avoiding walk (ISAW) model, which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either θ-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike swollen polymer phase (coil) and the low-temperature liquid-drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.

Collapse transition of self-avoiding trails on the square lattice

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, which map to a particular temperature of interacting self-avoiding trails, showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self-avoiding walks. On the other hand, it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model. In this work we simulate the standard equilibrium interacting self-avoiding trail model on the square lattice up to lengths over 2,000,000 steps and show that the results of the kinetic growth simulations are, in fact, entirely in accord with standard simulations of the temperature dependent model. In this way we verify that the collapse transition of interacting self-avoiding walks and trails are indeed in different universality classes in two dimensions.