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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…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario…
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension D interacting via an exclusion condition with a fixed impurity in d-dimensional Euclidean space in which the manifold is embedded. We…
We elaborate on the application of on-shell and unitarity-based methods for evaluating renormalization group coefficients, and generalize this framework to account for the mixing of operators with different dimensions and leading mass…
We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean…
A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in $d+1$ dimensions by dynamic renormalization group theory is described. The fixed points and exponents are calculated to two--loop order. We use the dimensional…
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…
We derive the three-loop order renormalization group equations that describe the flat phase of polymerized membranes within the modified minimal subtraction scheme, following the pioneering one-loop order computation of Aronovitz and…
We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is…
In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering…
A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations $\sim |{\bf x}|^{-a}$ for large separations ${\bf x}$ is given. Directly for three-dimensional systems and different…
We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $\beta$ functions…
For scalar QED on a three-dimensional toroidal lattice with a fine lattice spacing we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to…
We derive a universal formula for the one-loop renormalization of the effective K\"ahler potential that applies to general supersymmetric effective field theories of chiral multiplets, with arbitrary interactions respecting N=1…
We discuss the dependence of the results of renormalized perturbation theory for dilute polymer solutions on the choice of the uncritical manifold where the perturbation series are evaluated. Special emphasis is given to the influence of…
We study the behavior of self avoiding polymers in a background of vertically aligned rods that are either frozen into random positions or free to move horizontally. We find that in both cases the polymer chains are highly elongated, with…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…