Bachelor thesis – Kai Klede
Kai Klede
Ising model on finite projective geometries
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finished 2018-07
supervised by Klaus Mecke
Abstract
This thesis investigates the nearest neighbor Ising Model on two dimensional finite projective spaces, over finite fields of prime order. The neighborhood relation is de- fined by a flat biquadric field. When spins are placed only in the affine plane, the mean field critical exponents are found numerically via finite size scaling. The interpretation of these results suggests a notion of system size, proportional to the square root of the field order. The graph diameter as candidate for this system size is ruled out. A high temperature expansion of fifth order was not sufficient to extract the critical behavior analytically.
This thesis investigates the nearest neighbor Ising Model on two dimensional finite projective spaces, over finite fields of prime order. The neighborhood relation is de- fined by a flat biquadric field. When spins are placed only in the affine plane, the mean field critical exponents are found numerically via finite size scaling. The interpretation of these results suggests a notion of system size, proportional to the square root of the field order. The graph diameter as candidate for this system size is ruled out. A high temperature expansion of fifth order was not sufficient to extract the critical behavior analytically.