Related papers: Self-avoiding walks on a bilayer Bethe lattice
The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically by means of the Corner Transfer Matrix Renormalization Group algorithm. The critical…
We define the matching measure of a lattice L as the spectral measure of the tree of self-avoiding walks in L. We connect this invariant to the monomer-dimer partition function of a sequence of finite graphs converging to L. This allows us…
In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The…
We study the fully-packed dimer model on the bilayer square lattice with fugacity equal to $z$ ($1$) for inter-layer (intra-layer) dimers, and intra-layer interaction $V$ between neighbouring parallel dimers on any elementary plaquette in…
We use a simple lattice statistical model to analyze the effects of directional interactions on the phase diagram of a fluid of two-state Janus particles. The problem is formulated in terms of nonlinear recursion relations along the…
We study the model of a partially directed flexible or semi-flexible homopolymer on a square lattice, subject to an externally applied force, in a direction either parallel to, or perpendicular to the preferred direction. The polymer is…
Lipid monolayers and bilayers have been used as experimental models for the investigation of membrane thermal transitions. The main transition takes place near ambient temperatures for several lipids and reflects the order-disorder…
The paper presents a short overview of the theoretical, numerical and experimental works on the critical behavior of a dilute polymer solution of long-flexible polymer chains confined in semi-infinite space restricted by a surface or in a…
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model…
We study the problem of adsorption and collapse transition of a linear polymer chain situated in a fractal container represented by a 4-simplex lattice and interacting with a surface adsorbed linear polymer chain. The adsorbed chain…
We analyze the interaction of two conducting, charged polymer chains in solution using a minimal model for their electronic degrees of freedom. We show that a crossing of the two chains in which the polymers pass within Angstroms of each…
We present Monte Carlo simulations of semidilute solutions of long self-attracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
Using Brownian Dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order, (in the infinite chain…
In a bilayer system of fermionic dipoles, a full control over the strength of the attractive interactions between two layers leads to the BCS-BEC crossover. Here, using the BCS mean field theory, we study such a crossover in symmetric…
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer…
This research paper comprehensively explores the effects of molecular weight and chain architecture on the interfacial and thermodynamic properties of cyclic and linear polymer blends. Utilizing the Kremer-Grest bead-spring model, the study…
Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the…
We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence…
There are few exactly solvable lattice models and even fewer solvable quantum lattice models. Here we address the problem of finding the spectrum of the tight-binding model (equivalently, the spectrum of the adjacency matrix) on Cayley…