Collapse transition of self-avoiding trails on the square lattice

Abstract

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.

Cited by in corpus (16)

• Universality of collapsing two-dimensional self-avoiding trails
• Identification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymers
• Weighting of topologically different interactions in a model of two-dimensional polymer collapse
• Self-avoiding trails with nearest neighbour interactions on the square lattice
• Nature of the collapse transition in interacting self-avoiding trails
• Numerical simulation of a lattice polymer model at its integrable point
• Anomalous critical behaviour in the polymer collapse transition of three-dimensional lattice trails
• Surface critical behaviour of the Interacting Self-Avoiding Trail on the square lattice
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Semi-flexible interacting self-avoiding trails on the square lattice
• Lattice polymers with two competing collapse interactions
• The role of three-body interactions in two-dimensional polymer collapse
• Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge
• Adsorption of interacting self-avoiding trails in two dimensions
• Anomalous polymer collapse winding angle distributions
• Effect of lattice inhomogeneity on collapsed phases of semi-stiff ISAW polymers