Related papers: Mean-field tricritical polymers
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such a walk by studying the phase diagram…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The…
We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field…
We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…
We obtain the solution of models of self-avoiding walks with attractive interactions on Husimi lattices built with squares. Two attractive interactions are considered: between monomers on first-neighbor sites and not consecutive along a…
Magnetic polymers are examples of composite soft materials in which the competition between the large configurational entropy of the soft substrate (polymer) and the magnetic interaction may give rise to rich equilibrium phase diagrams as…
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically…
We study the one dimensional three species monomer-monomer reaction model in the reaction controlled limit using mean-field theory and dynamic Monte Carlo simulations. The phase diagram consists of a reactive steady state bordered by three…
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…
Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A…
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 geometric constraints on the ends of the polymer and…
We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a…
We consider two intimately related statistical mechanical problems on $\mathbb{Z}^3$: (i) the tricritical behaviour of a model of classical unbounded $n$-component continuous spins with a triple-well single-spin potential (the $|\varphi|^6$…
In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions…
The coil-globule transition of an isolated polymer has been well established to be a second-order phase transition described by a standard tricritical O(0) field theory. We present Monte-Carlo simulations of interacting self-avoiding walks…
We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
Insoluble surfactant monolayers at the air/water interface undergo a phase transition from a high-temperature homogeneous state to a low-temperature demixed state, where dilute and dense phases coexist. Alternatively, the transition from a…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…