A simulation framework for studying phase transitions, symmetry breaking, and transient dynamics in coupled field systems using Landau theory.
- Coupled Field Dynamics: Simulate two interacting fields (C and I) with quartic Landau potentials
- Automatic Adaptive Timestepping: Robust solver with backtracking for stiff equations
- Parameter Sweeps: Automated exploration of parameter space (β, s, κ, δ, etc.)
- Validation Pipeline: Built-in metrics for phase transition analysis and bias grading
- Reproducible: Seed control, frozen requirements, and full configuration logging
# Install dependencies
pip install -r requirements.txt
# Run a parameter sweep
python scripts/run_suite.py --matrix matrices/YOUR_MATRIX.csv --out runs_output/
# Generate summary and plots
python scripts/aggregate_final_summary.py --runs runs_output/ --out summary.csv
python scripts/plot_phase_maps.py --csv summary.csvThe system uses coupled Landau equations:
V(u) = (a/2)u² + (δ/4)u⁴ - su
∂C/∂t = -M_C [V'(C) - βI - κ_C∇²C]
∂I/∂t = -M_I [V'(I) - βC - κ_I∇²I]
| Parameter | Description |
|---|---|
s |
Symmetry-breaking tilt |
β |
Coupling strength between fields |
κ |
Surface tension / gradient penalty |
δ |
Quartic potential coefficient |
M |
Mobility / timescale |
├── scripts/ # Simulation, validation, and plotting scripts
├── uet_core/ # Core solver and energy functions
├── matrices/ # Parameter sweep configurations
├── docs/ # Documentation
└── requirements.txt # Dependencies
s > 0→ System biases toward C (BIAS_C)s < 0→ System biases toward I (BIAS_I)s = 0→ Random (50/50 symmetry)- Phase transition occurs at critical line s = 0
- Python 3.11+
- NumPy, SciPy, Matplotlib, Pandas
MIT License