The partition function for the problem of n directed non-intersecting walks interacting via contact potentials with a wall parallel to the direction of the walks has previously been calculated as anâ€¦ (More)

We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometricâ€¦ (More)

Abstract The number of free sites next to the end of a self-avoiding walk is known as the atmosphere of the walk. The average atmosphere can be related to the number of configurations. Here we studyâ€¦ (More)

The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been recently calculated. The walksâ€¦ (More)

We consider a network model, embedded on the Manhattan lattice, of a quantum localization problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disorderedâ€¦ (More)

We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted accordingâ€¦ (More)

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N = 16384, providing the first such results in dimensions d > 4 on which we concentrateâ€¦ (More)

The partition function for the problem of an arbitrary number of directed non-intersecting walks interacting with one or two walls parallel to the direction of the walks is calculated exactlyâ€¦ (More)

Much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk, polygon and animal models. The crossover exponent Ï† has been ofâ€¦ (More)

We present the solution of a linear solid-on-solid (SOS) model. Configurations are partially directed walks on a two-dimensional square lattice and we include a linear surface tension, a magneticâ€¦ (More)