Reproducible Julia simulations for central-height fluctuations in the Gamma-disordered Aztec diamond. The repository compares ordinary logarithmic growth with the super-rough squared-logarithmic prediction and separates conditional tiling noise from disorder-induced fluctuations using paired double-dimer samples.
The active project is aztec/. Earlier loop-erased-random-walk work
is preserved under old/ and is not required by the Aztec code.
Requirements: Julia 1.10 or newer. Only Julia standard libraries are used.
# Run all unit tests.
julia --project=aztec -e 'using Pkg; Pkg.test()'
# Reanalyse the retained single-height data.
julia --project=aztec aztec/scripts/analyze_height_campaign.jl
# Reanalyse the retained shared-environment pairs.
julia --project=aztec aztec/scripts/analyze_double_dimer_campaign.jlGenerated batches and scratch analyses go to the ignored aztec/output/
directory. Retained data, checksums, tables, and figures live in
aztec/data/ and aztec/results/.
- 35,536 independent single-height samples through order 1,300.
- 28,304 independent environments with two conditional tilings per environment, also through order 1,300.
- Deterministic per-sample seeds, atomic resumable batches, and 10,000-replicate within-size bootstrap analyses.
The total single-height data do not decisively distinguish the two affine curves. The double-dimer difference favours ordinary log over the full fitted range. The paired covariance, which directly estimates the disorder-induced variance, has suggestive upward curvature but remains noisy at the largest orders.
See the project guide for the model and commands, and the analysis report for numerical results and finite-size caveats.