Self-replicating functions and the renormalization group

TL;DR

This paper analyzes the limitations of block renormalization group techniques by examining a functional operator that formalizes self-replicability, focusing on the mathematical properties of its fixed points.

Contribution

It introduces a formal framework for understanding self-replicability in systems and analyzes the fixed points of the associated functional operator.

Findings

Fixed points of the operator are characterized mathematically.

The partial success of block renormalization is explained through this framework.

Abstract

The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The mathematical properties of the fixed points of this transformation are analyzed.