Bifurcation in correlation length of the Ising model on a "Toblerone" lattice

TL;DR

This paper investigates a decorated Ising ladder model, revealing a bifurcation in correlation lengths caused by eigenvalue crossing, which explains complex thermodynamic behaviors related to geometric frustration.

Contribution

The study uncovers a bifurcation in correlation lengths in a decorated Ising ladder, linking eigenvalue crossing to thermodynamic anomalies and geometric frustration effects.

Findings

Bifurcation in correlation lengths due to eigenvalue crossing.

Two distinct length scales for correlation decay.

Insights into thermodynamics influenced by geometric frustration.

Abstract

The classical Ising chain is the paradigm for the non-existence of phase transitions in 1D systems and was solved by Ernst Ising one hundred years ago. More recently, a decorated two leg Ising ladder has received interest for the curious thermodynamics that resemble a phase transition; a sharp peak in the specific heat at low, but finite temperature. We use this model to reveal a bifurcation in the correlation lengths due to a crossing of the sub-leading eigenvalues of the transfer matrix, which results in two distinct length scales necessary to describe to the decay of correlations. We discuss this phenomenon in the context of the geometric frustration in the model. We also provide additional results to aid in the understanding of the curious thermodynamics of the model through a study of the magnetic susceptibilities.