Related papers: Solution of a model of SAW's with multiple monomer…
Motivated by recent advances in transition metal dichalcogenide (TMD) moir\'e materials, we propose TMD moir\'e multilayers as a platform for realizing an approximately SU(4)-symmetric triangular Kondo lattice, generalizing the concept of…
Polymers in confined spaces are compressed and have reduced conformational entropy, and will partially or fully escape from confinement if conditions are suitable. This is in particular the case for a polymer grafted in a pore. The escape…
We have analyzed geometric and topological features of self-avoiding walks. We introduce a new kind of walk: the loop-deleted self-avoiding walk (LDSAW) motivated by the interaction of chromatin with the nuclear lamina. Its critical…
The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
The Hubbard model and extended Hubbard model on the honeycomb lattice can be seen as prototype models of single layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the…
We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length…
We study a model of continuous-time nearest-neighbor random walk on $\mathbb{Z}^d$ penalized by its occupation time at the origin, also known as a homopolymer. For a fixed real parameter $\beta$ and time $t>0$, we consider the probability…
We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive.…
We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical…
We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer…
The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods…
The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean…
We present an algorithm for the exhaustive enumeration of all monomer sequences and conformations of short lattice proteins as described by the hydrophobic-polar (HP) model. The algorithm is used for an exact identification of all designing…
The rotor-router model, also called the Propp machine, was introduced as a deterministic alternative to the random walk. In this model, a group of identical tokens are initially placed at nodes of the graph. Each node maintains a cyclic…
The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using DMRG and coupled with finite-size scaling. Particular attention is paid to the critical…
We study the polymer system consisting of two polymer chains situated in a fractal container that belongs to the three--dimensional Sierpinski Gasket (3D SG) family of fractals. Each 3D SG fractal has four fractal impenetrable 2D surfaces,…
We introduce classes of restricted walks, surfaces and their generalisations. For example, self-osculating walks (SOWs) are supersets of self-avoiding walks (SAWs) where edges are still not allowed to cross but may 'kiss' at a vertex. They…
Some time ago Salmhofer demonstrated the equivalence of the strong coupling lattice Schwinger model with Wilson fermions to a certain 8-vertex model which can be understood as a self-avoiding loop model on the square lattice with bending…
We construct the two-sided infinite self-avoiding walk (SAW) on $\mathbb{Z}^d$ for $d\geq5$ and use it to prove pattern theorems for the self-avoiding walk. We show that infinite two-sided SAW is the infinite-shift limit of infinite…