Relevant Aperiodic Modulation in the 2d Ising Model

TL;DR

This paper investigates how aperiodic Rudin-Shapiro sequence modulations affect the surface critical behavior of a 2D Ising model, revealing unusual critical properties including discontinuous or singular surface magnetization.

Contribution

It provides an exact analysis of the surface critical behavior in a 2D Ising model with aperiodic couplings, highlighting novel critical phenomena caused by Rudin-Shapiro modulation.

Findings

Surface magnetization is either discontinuous or vanishes with an essential singularity.

Critical properties depend on the strength of the aperiodic modulation.

Exact calculations of the surface magnetization and singularity form are presented.

Abstract

We consider the surface critical behaviour of a semi-infinite two-dimensional layered Ising model, where the couplings perpendicular to the surface follow the aperiodic Rudin-Shapiro sequence. The model has unusual critical properties: depending on the strength of the modulation, at the bulk critical point the surface magnetization is either discontinuous or vanishes with an essential singularity. The critical surface magnetization as well as the form of the essential singularity are calculated exactly.