181 citations · 1.9k across the 66 of their papers we have counts for
15 papers · 1 filter
Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices
Anthony J Guttmann, Iwan Jensen
We have analysed the recently extended series for the number of self-avoiding walks (SAWs) that cross an square between diagonally opposed corners. The number…
Self-avoiding walks contained within a square
Anthony J Guttmann, Iwan Jensen, Aleksander L Owczarek
We have studied self-avoiding walks contained within an square whose end-points can lie anywhere within, or on, the boundaries of the square. We prove that such walks…
On the existence of critical exponents for self-avoiding walks
Anthony J Guttmann, Iwan Jensen
We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctne…
Three friendly walkers
Iwan Jensen
More than 15 years ago Guttmann and Vöge [J. Statist. Plann. Inference, {\bf 101}, 107 (2002)], introduced a model of friendly walkers. Since then it has remained unsolved. In this…
Compressed self-avoiding walks, bridges and polygons
Nicholas R. Beaton, Anthony J. Guttmann, Iwan Jensen +1
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or ve…
Integrability vs non-integrability: Hard hexagons and hard squares compared
M. Assis, J. L. Jacobsen, I. Jensen +2
In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consi…