Structure Function of Ising Model on a Penrose Tiling

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Structure Function of Ising Model on a Penrose
Tiling

• By Helen Au-Yang and
• Jacques H.H. Perk

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Half of the sites of a Penrose tiling interact as
indicated by the lines. The other sites play no
role.
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Summary More and more peaks visible as
temperature decreases toward critical
point.(Last picture shows behavior at larger
q-values.)
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Intensity is quasiperiodic Does not exactly
repeat. But, note how corners are already similar
to center.Also, note the ten-fold symmetry
around the center.
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Detail near central intensity peakAverage
correlation length 2,further from critical
temperature.
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Detail near central intensity peakAverage
correlation length 4,less far from critical
temperature.
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Detail near central intensity peakAverage
correlation length 8,nearest to critical
temperature.