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

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.

24 pages, 16 figures. Further references added, misprints corrected, additional points added to conclusions, some ambiguities clarified

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Cited by in corpus (4)

• Quantum Otto engine mimicking Carnot near pseudotransitions in the one-dimensional extended Hubbard model in the atomic limit
• Dual thermal pseudocritical features in a spin-1/2 Ising chain with twin-diamond geometry
• Thermodynamic constraints and pseudotransition behavior in a one-dimensional water-like system
• The Widom line in the Ising model on a decorated bilayer lattice