Related papers: Collapse of a polymer in two dimensions
Polymer chains undergoing a continuous adsorption-desorption transition are studied through extensive computer simulations. A three-dimensional self-avoiding walk lattice model of a polymer chain grafted onto a surface has been treated for…
We use complete enumeration and Monte Carlo techniques to study two-dimensional self-avoiding polymer chains with quenched ``charges'' $\pm 1$. The interaction of charges at neighboring lattice sites is described by $q_i q_j$. We find that…
This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used…
We study a statistical ensemble of a single polymer with self gravitational interaction. This is a model of a gravitating string --- the precursor of a black hole. We analyze averaged sizes by mean field approximations with an effective…
Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…
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…
Exact results for conformational statistics of compact polymers are derived from the two-flavour fully packed loop model on the square lattice. This loop model exhibits a two-dimensional manifold of critical fixed points each one…
We have studied the transition in shape of two dimensional polyampholytes using Monte Carlo simulation. We observe that polymers with randomly charged monomers get into a globular shape at lower temperatures, provided that their total…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…
There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours. This difference has been without a clear explanation. The collapse transition has been variously seen to be in the…
The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive…
We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are…
We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the…
Extensive molecular dynamics simulations were conducted to explore the conformational phase diagram of a neutral polymer in the presence of attractive crowders of varying sizes. For weakly self-attractive polymers, larger crowders induce a…
We study the scaling limit of a fully packed loop model in two dimensions, where the loops are endowed with a bending rigidity. The scaling limit is described by a three-parameter family of conformal field theories, which we characterize…
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…
A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts model interacts with the strength $J(>0)$ in the $xy$-plane and with $\lambda J$ $(0\le \lambda \ll 1)$ in the $z$-axis. The phase transition is of second-order…
We present an in-depth multi-scale analysis of the conformations and dynamics of polar active polymers, comparing very dilute and very dense conditions. We unveil characteristic length and time scales, common to both dilute and dense…