Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents

Correction-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks

We study the correction-to-scaling exponents for the two-dimensional selfavoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a mon...

Two-dimensional self-avoiding walks and polymer adsorption: critical fugacity estimates

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is 1 + √ 2. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the ab...

Continuously Varying Exponents for Oriented Self-avoiding Walks

A two-dimensional conformal field theory with a conserved U(1) current ~ J , when perturbed by the operator ~ J 2, exhibits a line of fixed points along which the scaling dimensions of the operators with non-zero U(1) charge vary continuously. This result is applied to the problem of oriented polymers (self-avoiding walks) in which the short-range repulsive interactions between two segments dep...

Two-dimensional oriented self-avoiding walks with parallel contacts

Oriented self-avoiding walks (OSAWs) on a square lattice are studied, with binding energies between steps that are oriented parallel across a face of the lattice. By means of exact enumeration and Monte Carlo simulation, we reconstruct the shape of the partition function and show that this system features a first-order phase transition from a free phase to a tight-spiral phase at βc = log(μ), w...

Self-interacting self-avoiding walks on the Sierpinski gasket