Related papers: Relating Theories via Renormalization
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of…
Nonrenormalizable quantum field theories require counterterms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counterterms suggested by renormalized perturbation…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding…
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the…
An introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics is presented in the form of 6 lectures delivered to the British Universities Summer School in Theoretical…
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
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 as well as number theory and…