Two-dimensional oriented self-avoiding walks with parallel contacts

Abstract

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 ${\beta }_c=\log (\mu )$, where $\mu =2.638$ is the growth constant for SAWs. With Monte Carlo simulations we show that parallel contacts happen predominantly between a step close to the end of the OSAW and another step nearby; this appears to cause the expected number of parallel contacts to saturate at large lengths of the OSAW.

12 pages, revtex, 10 separate PostScript figures

References in corpus (3)

• Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice
• Continuously Varying Exponents for Oriented Self-Avoiding Walks
• Oriented Polymers: A Transfer Matrix Calculation

Cited by in corpus (5)

• Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice
• Zipping and collapse of diblock copolymers
• 2-d Self-Avoiding Walks on a Cylinder
• On the Non-Universality of a Critical Exponent for Self-Avoiding Walks
• Winding angles for two-dimensional polymers with orientation dependent interactions