Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation

TL;DR

This paper studies concentric circular defects in the 2D Ising model with a generalized Fredholm sequence, revealing how aperiodic perturbations affect local magnetization and confirming the gap-exponent relation's validity.

Contribution

It introduces a novel analysis of aperiodic radial defects in the Ising model and demonstrates the continuous variation of the local magnetization exponent.

Findings

Local magnetization exponent varies continuously with modulation amplitude.

The gap-exponent relation remains valid despite aperiodic defects.

Critical bulk behavior remains unchanged by the aperiodic perturbation.

Abstract

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetization is obtained through finite-size scaling, using a corner transfer matrix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen model. Through a conformal mapping of the system onto a strip, the gap-exponent relation is shown to remain valid for such an aperiodic defect.