Related papers: N=2 Supersymmetry, Painleve III and Exact Scaling …
Recently the scaling function of the dilute non-contractible self-avoiding 2D polymer loop on a cylinder was related to the Painleve III transcendent. Using the perturbation theory, the thermidynamic Bethe ansatz and numerical calculations…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
We investigate the matrix model with weight $w(x):=\exp(-z^2/2x^2 + t/x - x^2/2)$ and unitary symmetry. and unitary symmetry. In particular we study the double scaling limit as $N \to \infty$ and $(\sqrt{N} t, Nz^2 ) \to (u_1,u_2)$, where…
Equilibrium states of a closed semiflexible polymer binding to a cylinder are described. This may be either by confinement or by constriction. Closed completely bound states are labeled by two integers: the number of oscillations, $n$, and…
We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…
The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by $H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx +…
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…
A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of non-contractible loops with a fixed fugacity $\xi$, the model is a generalization of the critical dense polymers solved…
As a step towards deriving universal amplitude ratios of the superconductive phase transition we calculate the vacuum energy density in the symmetric phase of O(N)-symmetric scalar QED in D=4-epsilon dimensions in an epsilon-expansion using…
We examine the scaling of the linear dimension of the system size of a real polymer solution at constant excess free energy and in two different spacial dimensionalities, d=d0 and d=d1. Standard results for the functional form of the excess…
$O(N)$ invariant vector models have been shown to possess non-trivial scaling large $N$ limits, at least perturbatively within the loop expansion, a property they share with matrix models of 2D quantum gravity. In contrast with matrix…
Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization the true two-line ground-state is compared with the single line ground state plus its first excited state. It is found…
The relaxational dynamics of 1+1 dimensional directed polymer in random potential is studied by Monte Carlo simulation. A series of temperature quench experiments is performed changing waiting times. Clear crossover from quasi-equilibrium…
We investigate $O(N)$-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in $D$ dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random…
Dimensional reduction of high temperature field theories improves IR features of their perturbative treatment. A crucial question is, what three-dimensional theory is representing the full system the most faithful way. Careful investigation…
We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation…
A variational framework is developed to examine the equilibrium states of a semi-flexible polymer that is constrained to lie on a fixed surface. As an application the confinement of a closed polymer loop of fixed length $2\pi R$ within a…
This paper considers an undirected polymer chain on $\mathbb{Z}^d$, $d \geq 2$, with i.i.d.\ random charges attached to its constituent monomers. Each self-intersection of the polymer chain contributes an energy to the interaction…
Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy $F$ is measured as a…
We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the…