Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems

TL;DR

This study examines how aperiodic sequences affect the critical behavior of layered 2D Ising models, comparing bond and site problems, and extends relevance criteria to include surface magnetization effects.

Contribution

It introduces an extended relevance-irrelevance criterion for aperiodic perturbations, applicable to both bond and site problems, and analyzes surface magnetization for specific sequences.

Findings

Surface magnetization varies with aperiodic sequences.

Extended criterion predicts relevance of aperiodic perturbations.

Differences observed between bond and site problem behaviors.

Abstract

We investigate the influence of aperiodic perturbations on the critical behaviour at a second order phase transition. The bond and site problems are compared for layered systems and aperiodic sequences generated through substitution. In the bond problem, the interactions between the layers are distributed according to an aperiodic sequence whereas in the site problem, the layers themselves follow the sequence. A relevance-irrelevance criterion introduced by Luck for the bond problem is extended to discuss the site problem. It involves a wandering exponent for pairs, which can be larger than the one considered before in the bond problem. The surface magnetization of the layered two-dimensional Ising model is obtained, in the extreme anisotropic limit, for the period-doubling and Thue-Morse sequences.