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We study close-packed dimers on the quasiperiodic Ammann-Beenker (AB) graph,that was recently shown to have the unusual feature that hard-core dimerconstraints are exactly reproduced at successive discrete length scales. Thisobservation led to a conjecture that it would be possible to construct an exactreal-space decimation scheme where each iteration preserves both thequasiperiodic tiling structure and the constraint. Here, we confirm thisconjecture by explicitly constructing the corresponding renormalization grouptransformation and show, using large-scale Monte Carlo simulations, that thedimer distributions flow to a fixed point with non-zero dimer potentials. Weuse the fixed-point Hamiltonian to demonstrate the existence of slowly decayingdimer correlations. We thus identify a remarkable example of a classicalstatistical mechanical model whose properties are controlled by the fixed pointof an exact renormalization group procedure exhibiting discrete scaleinvariance but lacking translational and continuous rotational symmetries.

Discrete scale invariant fixed point in a quasiperiodic classical dimer model