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Efficient simulation of spin systems in Rust

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# PeaPods

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A Python library for simulating Ising spin systems with modern Monte Carlo methods.
The core simulation loop is written in Rust (via PyO3) for performance, with a thin Python wrapper for ease of use.
Currently focused on spin glass simulation, where the combination of parallel tempering, replica cluster moves, and overlap statistics is of particular interest.

## Features

- Ising ferromagnets and spin glasses on periodic Bravais lattices (hypercubic, triangular, or any custom neighbor offsets)
- Arbitrary, bimodal (±J), or Gaussian coupling distributions
- Multiple replicas with overlap statistics for spin glass order parameters

The following algorithms are currently supported:

- Single-spin flips ([Metropolis](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) and [Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling))
- [Swendsen-Wang cluster updates](https://en.wikipedia.org/wiki/Swendsen%E2%80%93Wang_algorithm)
- [Wolff cluster updates](https://en.wikipedia.org/wiki/Wolff_algorithm)
- [Parallel tempering](https://en.wikipedia.org/wiki/Parallel_tempering)
- [Houdayer isoenergetic cluster move](https://arxiv.org/abs/cond-mat/0101116) (replica cluster move for spin glasses)
- [Jörg move](https://arxiv.org/abs/cond-mat/0410328) (stochastic overlap cluster move)
- [CMR move](https://doi.org/10.1103/PhysRevE.62.8114) (Chayes-Machta-Redner blue-bond overlap cluster move)
- Passive full-graph FK and overlap-cluster observations with per-disorder statistics
- Full-ladder parallel tempering diagnostics and reproducible optional seeds

## Quickstart

Run simulations directly from the terminal:

```bash
# 2D ferromagnet with cluster updates and parallel tempering
peapods simulate --shape 32 32 --temp-min 1.5 --temp-max 3.0 \
    --n-sweeps 5000 --cluster-interval 1 --pt-interval 1 --n-replicas 2

# 3D spin glass with Houdayer ICM
peapods simulate --shape 8 8 8 --couplings bimodal \
    --temp-min 0.8 --temp-max 1.4 --n-temps 24 --n-sweeps 10000 \
    --pt-interval 1 --overlap-cluster-update-interval 1 --n-replicas 4

# Save full results to .npz
peapods simulate --shape 16 16 --temp-min 1.5 --temp-max 3.0 \
    --n-sweeps 5000 --pt-interval 1 --n-replicas 2 -o results.npz
```

For full control over geometry and parameters, use the Python API directly:

```python
import numpy as np
from peapods import Ising

# Triangular lattice ferromagnet (T_c = 4/ln(3) ≈ 3.641)
tri = Ising((32, 32), temperatures=np.linspace(3.0, 4.2, 32),
            n_replicas=2, neighbor_offsets=[[1, 0], [0, 1], [1, -1]])
tri.sample(n_sweeps=5000, sweep_mode="metropolis",
           cluster_update_interval=1, pt_interval=1)
print(tri.binder_cumulant)
```

Pass an explicit seed for deterministic couplings and dynamics. Full SW-style
graphs can be measured without acting on spins:

```python
model = Ising((32, 32), couplings="bimodal", temperatures=np.linspace(1, 3, 16),
              n_replicas=2, seed=42)
result = model.sample(n_sweeps=5000, cluster_update_interval=10,
                      cluster_mode="sw", cluster_action="observe",
                      pt_interval=1, pt_schedule="full_ladder")
fk = result["per_disorder"]["cluster_observations"]["fk"]
```

Autocorrelation diagnostics use the exact bounded-memory ring backend by
default. Set `autocorrelation_backend="fft"` together with
`autocorrelation_max_lag` for faster evaluation when retaining the full
measurement history and its higher memory use are acceptable.

For a more complete example, check out [examples/energy_vs_temperature.py](examples/energy_vs_temperature.py).

## Installation

We recommend [uv](https://docs.astral.sh/uv/) for package management. Bare `pip` works too (if you don't mind using a worse management tool).

```bash
uv venv
source .venv/bin/activate
uv pip install peapods
```

Pre-built wheels are available for Linux (x86_64, aarch64), macOS (Intel, Apple Silicon), and Windows (x86_64).

## Building from source

Requires a Rust toolchain and [maturin](https://www.maturin.rs/):

```bash
uv pip install maturin numpy
maturin develop --release
```

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