We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on Zd, having long finite-range connections, above their upper critical dimensions d = 4 (self-avoiding walk), d = 6 (percolation) and d = 8 (trees and animals). The two-point functions for these models are respectively the generating function for selfavoiding walks from the origin to x...

The effect of rotational constraint on the properties of lattice models like the self-avoiding walk, lattice animals and percolation is discussed. The results obtained so far, using a variety of exact and approximate techniques, are described. Examples of the rotational constraint in real systems are also given.

We consider nearest-neighbour self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on Z. The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to x ∈ Z, the probability of a connection from the origin to x, and the generating functions for lattice trees or lattice animals containing the origin and x. Usi...

This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative analysis of a supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on Zd. We now present an analysis of the relevant inter...

For self-avoiding walks on the d-dimensional cubic lattice defined with a positive bias in one of the coordinate directions, it is proved that the drift in the favored direction is strictly positive. c © 2008 Elsevier B.V. All rights reserved. Keyword: Biased self-avoiding walks

Restitution is a monetary remedy paid by perpetrator or third party to victim their family. It can be implemented returning property, payment for losses suffering, reimbursement of costs. However, restitution not applicable all types crimes; thus, victims have access it.The issue legal protection still an ongoing discourse, and many parties believe that its implementation far from perfect in ne...

Prudent walks are self-avoiding walks on a lattice which never step into the direction of an already occupied vertex. We study the closed version of these walks, called prudent polygons, where the last vertex of the walk is adjacent to its first one. More precisely, we give the half-perimeter generating functions of two subclasses of prudent polygons on the square lattice, which turn out to be ...

I use a Landau theory to study the behavior of A – B heteropolymers with disordered sequences immersed in a binary solvent mixture. Segments of type A are preferentially solvated in one type of solvent, and those of type B prefer the other type of solvent. At high temperatures, the behavior is qualitatively the same as that in a single solvent. As the temperature approaches the critical tempera...

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is 1 + √ 2. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the ab...

We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice Zd. The method is based on loop erasure and restoration, and does not require exact enumeration data. Our bounds are best for high d, and in fact agree with the rst four terms of the 1=d expansion for the connective constant. The bounds are the best t...