130 citations · 2k across the 94 of their papers we have counts for
22 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…
Statistical Mechanics of Confined Polymer Networks
Bertrand Duplantier, Anthony J Guttmann
We show how the theory of the critical behaviour of -dimensional polymer networks of arbitrary topology can be generalized to the case of networks confined by hyperplanes. This…
Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
A. J. Guttmann, I. Jensen, J-M. Maillard +1
We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determin…
Automata and the susceptibility of the square lattice Ising model modulo powers of primes
A. J. Guttmann, J-M. Maillard
We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some les…