Related papers: Renormalization Theory for the Self-Avoiding Polym…
We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to…
We study the scaling limit of a model of a tethered crumpled D-dimensional random surface interacting through an exclusion condition with a fixed impurity in d-dimensional Euclidean space by the methods of Wilson's renormalization group. In…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
A model considered in the paper generalizes membrane theory to the case of delocalized membranes. The model admits covariant formulation, which involves no constraints. It generalizes the notion of membrane to the case of smooth…
An elastic membrane that is forced to reside in a container smaller than its natural size will deform and, upon further volume reduction, eventually crumple. The crumpled state is characterized by the localization of energy in a complex…
We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We develop a unified scaling framework for the end-position distributions of tethered polymers confined in finite cylindrical geometries. Two observables are analysed: the longitudinal distribution P(x), along the confinement axis, and the…
We investigate hexatic membranes embedded in Euclidean D-dimensional space using a reparametrization invariant formulation combined with exact renormalization group (RG) equations. An XY-model coupled to a fluid membrane, when integrated…
In this paper, we show how the method of field theoretical renormalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on…
It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem,…
Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model,…
A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…
We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a…
The scaling behavior of fully flexible elastic tethered surfaces has been debated for decades. Some theories predict that self-avoiding surfaces would crumple in the absence of bending rigidity, while most simulations suggested that they…
A remarkable property of flexible self-avoiding elastic surfaces (membranes) is that they remain flat at all temperatures, even in the absence of a bending rigidity or in the presence of active fluctuations. Here, we report numerical…
Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a…
Previous theories of dilute polymer solutions have failed to distinguish clearly between two very different ways of taking the long-chain limit: (I) $N \to\infty$ at fixed temperature $T$, and (II) $N \to\infty$, $T \to T_\theta$ with $x…