Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

TL;DR

This paper investigates the q-dependent susceptibility in quasiperiodic Ising models on square lattices, revealing that susceptibility peaks are generally periodic and only become incommensurate under specific mixed interaction or aperiodic lattice conditions.

Contribution

It extends the understanding of susceptibility behavior in quasiperiodic Ising models by analyzing various aperiodic sequences and generalizing key identities and theorems.

Findings

Susceptibility peaks are periodic and aligned with regular Ising models.

Incommensurate peaks only occur with mixed interactions or aperiodic lattices.

Peak positions vary significantly with different aperiodic sequences.

Abstract

We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.