Enumeration of self avoiding trails on a square lattice using a transfer matrix technique

Abstract

We describe a new algebraic technique, utilising transfer matrices, for enumerating self-avoiding lattice trails on the square lattice. We have enumerated trails to 31 steps, and find increased evidence that trails are in the self-avoiding walk universality class. Assuming that trails behave like $A{\lambda }^n{n}^{\frac{11}{32}}$, we find $\lambda =2.72062\pm 0.000006$ and $A=1.272\pm 0.002$.

To be published in J. Phys. A:Math Gen. Pages: 16 Format: RevTeX

References in corpus (1)

• Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice

Cited by in corpus (6)

• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
• Correction-to-scaling exponents for two-dimensional self-avoiding walks
• Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice
• SAWdoubler: a program for counting self-avoiding walks
• Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
• Structure factor of dilute ring polymers