Q-Dependent Susceptibility in Z-Invariant Pentagrid Ising Model

Abstract

We study the q-dependent susceptibility chi(q) of a Z-invariant ferromagnetic Ising model on a Penrose tiling, as first introduced by Korepin using de Bruijn's pentagrid for the rapidity lines. The pair-correlation function for this model can be calculated exactly using the quadratic difference equations from our previous papers. Its Fourier transform chi(q) is studied using a novel way to calculate the joint probability for the pentagrid neighborhoods of the two spins, reducing this calculation to linear programming. Since the lattice is quasiperiodic, we find that chi(q) is aperiodic and has everywhere dense peaks, which are not all visible at very low or high temperatures. More and more peaks become visible as the correlation length increases--that is, as the temperature approaches the critical temperature.

LaTeX2e, 52 pages, 12 figures (45 eps files), uses rotating.sty (choose right rotdriver). v2: Quality of figures has been much enhanced. v3: Misprints corrected

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• A critical Ising model on the Labyrinth
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Cited by in corpus (4)

• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• Classical Dimers on Penrose Tilings
• Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models
• Quasicrystals -- The impact of N.G. de Bruijn