Wavevector-Dependent Susceptibility in <Emphasis Type="Italic">Z</Emphasis>-Invariant Pentagrid Ising Model |
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Authors: | Helen Au-Yang Jacques H H Perk |
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Institution: | (1) Department of Physics, Oklahoma State University, Stillwater, OK 74078-3072, USA |
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Abstract: | We study the q-dependent susceptibility χ(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 χ(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 χ(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.
Supported in part by NSF Grant No. PHY 01-00041. |
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Keywords: | Ising model quasiperiodicity Fibonacci sequence pentagrid Penrose tiles Z-invariance correlation functions q-dependent susceptibility |
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