Discrete scale invariance, and its logarithmic extension

TL;DR

This paper explores discrete scale invariance and its logarithmic extension, analyzing how these symmetries influence correlation functions and discussing potential generalizations like translation and inversion.

Contribution

It provides a detailed investigation of the correlation functions under discrete scale symmetry and proposes extensions such as translation and inversion symmetries.

Findings

Discrete scale invariance causes log-periodic corrections to scaling.

General forms for correlation functions under these symmetries are derived.

Extensions like translation and inversion of the symmetry are discussed.

Abstract

It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and inversion, and find general forms for correlation functions.