Geometrical Properties of Two-Dimensional Interacting Self-Avoiding Walks at the Theta-Point

Abstract

We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point temperature T_theta = 1.4986(11), and several invariant size ratios. Then, we focus on the geometrical features of the walks, computing the instantaneous shape ratios, the average asphericity, and the end-to-end distribution function. For the latter quantity, we verify in detail the theoretical predictions for its small- and large-distance behavior.

23 pages, 4 figures

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Cited by in corpus (14)

• Collapse transition of a square-lattice polymer with next nearest-neighbor interaction
• The Generic Critical Behaviour for 2D Polymer Collapse
• Trapping in Self-Avoiding Walks with Nearest-Neighbor Attraction
• Theta-point polymers in the plane and Schramm-Loewner evolution
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
• Critical and geometric properties of magnetic polymers across the globule-coil transition
• Lattice polymers with two competing collapse interactions
• Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge
• Statistical Mechanics of Confined Polymer Networks
• Energy of the Interacting Self-Avoiding Walk at the $\theta -$point
• Winding angle distributions for two-dimensional collapsing polymers
• Randomly branching $\theta$-polymers in two and three dimensions: Average properties and distribution functions
• Anomalous polymer collapse winding angle distributions