Planar quasiperiodic Ising models

TL;DR

This paper studies zero-field Ising models on quasiperiodic tilings using partition function zeros and high-temperature expansions, providing insights into critical temperatures and universality class compatibility.

Contribution

It introduces a determinant-based method to analyze quasiperiodic Ising models and estimates their critical temperatures with high precision.

Findings

Critical temperature estimates align with theoretical predictions.

Results support Onsager universality in quasiperiodic systems.

Partition function zeros effectively identify phase transition points.

Abstract

We investigate zero-field Ising models on periodic approximants of planar quasiperiodic tilings by means of partition function zeros and high-temperature expansions. These are obtained by employing a determinant expression for the partition function. The partition function zeros in the complex temperature plane yield precise estimates of the critical temperature of the quasiperiodic model. Concerning the critical behaviour, our results are compatible with Onsager universality, in agreement with the Harris-Luck criterion based on scaling arguments.