Collapse of a polymer in two dimensions

Abstract

We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the basis of the O($n$) loop model in the limit $n\to 0$. It yields finite-size results for the magnetic correlation length of systems with a cylindrical geometry. A comparison with the predictions of finite-size scaling enables us to obtain information about the phase diagram as a function of the chemical potential of the loop segments and the strength of the attractive potential. Results for the magnetic scaling dimension can be interpreted in terms of known universality classes. In particular, when the attractive potential is increased, we observe the crossover between polymer critical behaviour of the self-avoiding walk type to behaviour described earlier for the theta point.

11 pages, Latex, 3 eps figs, Elsevier style files, to appear in the Hans van Leeuwen Festschrift (Physica A)

Cited by in corpus (11)

• Loop models with crossings
• Corner transfer matrix renormalization group method for two-dimensional self-avoiding walks and other O(n) models
• Phase Diagram of a Loop on the Square Lattice
• Weighting of topologically different interactions in a model of two-dimensional polymer collapse
• The Generic Critical Behaviour for 2D Polymer Collapse
• Exact characterization of O(n) tricriticality in two dimensions
• Ising-like transitions in the O($n$) loop model on the square lattice
• Crossover phenomena involving the dense O($n$) phase
• First and second order transitions in dilute O(n) models
• Critical properties of a dilute O($n$) model on the kagome lattice
• Special transitions in an O($n$) loop model with an Ising-like constraint