Related papers: Field Theory And Second Renormalization Group For …
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B.…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We propose a phenomenological field theoretical approach to the chemical etching of a disordered-solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
The renormalization of effective potential for the noncommutative scalar field theory is investigated to the two-loop approximation. It is seen that the nonplanar diagram does not appear in the one-loop potential. However, nonplanar diagram…
We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
A modified gravitational theory is developed in which the gravitational coupling constants $G$ and $Q$ and the effective mass $m_\phi$ of a repulsive vector field run with momentum scale $k$ or length scale $\ell =1/k$, according to a…
This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the the ultraviolet problem for the scalar phi^4 model on toroidal lattice in dimension d=3. In this second…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into…
We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory…