Log-periodic critical amplitudes: a perturbative approach

TL;DR

This paper presents a perturbative method to compute log-periodic critical amplitudes arising from systems with discrete scale invariance, especially near monomial renormalization maps, including subdominant corrections.

Contribution

It introduces a novel perturbative approach to calculate log-periodic amplitudes from near-monomial renormalization maps, extending understanding of critical behaviors.

Findings

Perturbative formulas for critical amplitudes derived

Method applicable to systems with discrete scale invariance

Calculations include subdominant correction amplitudes

Abstract

Log-periodic amplitudes appear in the critical behavior of a large class of systems, in particular when a discrete scale invariance is present. Here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial. In this case, the log-periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated.