Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains

TL;DR

This paper analytically calculates log-periodic amplitudes of surface magnetization in aperiodic Ising quantum chains, revealing how discrete scale invariance influences oscillating behaviors near critical points.

Contribution

It provides exact analytical results for log-periodic corrections in two types of aperiodic quantum chains, highlighting the effects of marginal and relevant perturbations.

Findings

Log-periodic amplitudes are derived analytically.

Oscillating behavior linked to discrete scale invariance.

Critical surface magnetization analyzed for different sequences.

Abstract

Log-periodic amplitudes of the surface magnetization are calculated analytically for two Ising quantum chains with aperiodic modulations of the couplings. The oscillating behaviour is linked to the discrete scale invariance of the perturbations. For the Fredholm sequence, the aperiodic modulation is marginal and the amplitudes are obtained as functions of the deviation from the critical point. For the other sequence, the perturbation is relevant and the critical surface magnetization is studied.