Related papers: Relating Theories via Renormalization
Correlators describing the vulcanization transition are constructed and explored via a renormalization group approach. This approach is based on a minimal model that accounts for the thermal motion of constituents and the quenched random…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
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…
It is shown that the Sigma-Omega model which is widely used in the study of nuclear relativistic many-body problem can exactly be treated as an Abelian massive gauge field theory. The quantization of this theory can perfectly be performed…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We study the information content of the reduced density matrix of a region in quantum field theory that cannot be recovered from its subregion density matrices. We reconstruct the density matrix from its subregions using two approaches:…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper,…
A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
This book provides an introduction to a renormalisation group method in the spirit of that of Wilson. It starts with a concise overview of the theory of critical phenomena and the introduction of several tools required in the…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…