Surface Magnetisation and Surface Correlations in Aperiodic Ising Models

TL;DR

This paper investigates how aperiodic sequences in layered Ising models affect surface critical behavior, revealing continuous variation of critical exponents and anisotropic scaling at criticality.

Contribution

It provides analytical and numerical methods to evaluate surface magnetization and correlations in aperiodic layered Ising models, highlighting the impact of aperiodicity on critical phenomena.

Findings

Surface magnetization evaluated analytically.

Surface correlations obtained numerically.

Critical exponents vary continuously with aperiodicity.

Abstract

We consider the surface critical behaviour of diagonally layered Ising models on the square lattice where the inter-layer couplings follow some aperiodic sequence. The surface magnetisation is analytically evaluated from a simple formula derived by the diagonal transfer matrix method, while the surface spin-spin correlations are obtained numerically by a recursion method, based on the star-triangle transformation. The surface critical behaviour of different aperiodic Ising models are found in accordance with the corresponding relevance-irrelevance criterion. For marginal sequences the critical exponents are continuously varying with the strength of aperiodicity and generally the systems follow anisotropic scaling at the critical point.