Partition function zeros of adsorbing self-avoiding walks
نویسنده
چکیده
Abstract. Partition function or Fisher zeros play a fundamental role in the theory of phase transitions in models in classical statistical mechanics. In this paper the properties of partition function zeros in a square lattice self-avoiding walk model of polymer adsorption are presented. Some results constraining the distribution of zeros in the complex plane, based on mathematical results on the distribution of polynomial zeros, are presented. Numerical results on the distribution of zeros are shown, based on approximate enumeration of square lattice walks using the GAS algorithm.
منابع مشابه
Compressed self-avoiding walks, bridges and polygons
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 vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all ver...
متن کاملTwo-dimensional oriented self-avoiding walks with parallel contacts
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 βc = log(μ), w...
متن کاملScaling of self-avoiding walks in high dimensions
We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte Carlo simulations up to length N = 16 384, providing the first such results in dimensions d > 4 on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results...
متن کاملA note on the corrections-to-scaling for the number of nearest neighbour contacts in self-avoiding walks
Recently, an exhaustive study has been made of the corrections-to-scaling for the number of, and various size measures (eg. radius of gyration) of, self-avoiding walks on the various two-dimensional lattices. This study gave compelling evidence that the first non-analytic correction-to-scaling has exponent Δ1 = 3/2. However, there also exist predictions in the literature for the corrections-to-...
متن کاملFinite-size scaling functions for directed polymers
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 walks can be considered to model the polymerinduced steric stabilization and sensitized flocculation of colloidal dispersions. The large-width asymptotics led to a phase diagram different to that of a polym...
متن کامل