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mcising

High-performance Ising model Monte Carlo simulation with a Rust core.

mcising is a Python library for Monte Carlo simulation of Ising spin systems. It supports 5 lattice geometries, J1-J2-J3 frustrated magnetism with external fields, 3 Monte Carlo algorithms, 3 execution modes (including parallel tempering), and adaptive thermalization. The performance-critical core is written in Rust via PyO3.

Why mcising

Who it is for. Researchers in computational and statistical physics who need classical Ising Monte Carlo they can trust and cite: studies of frustrated magnetism (competing J1-J2-J3 couplings on square, triangular, honeycomb and cubic lattices), critical phenomena and finite-size scaling, and machine-learning-for-physics work that needs large, labelled, reproducible sets of spin configurations.

The gap it fills. Textbook Ising codes are easy to write and hard to get right: the sign of a coupling, the neighbour table of a non-square lattice, the error bar on a specific heat. mcising packages the parts that go wrong as tested, pip-installable infrastructure — a Rust core checked against exact enumeration of small systems and against exact results (Onsager's solution, the critical temperatures of four lattices) on large ones; blocking and jackknife errors on every observable, with integrated autocorrelation times and adaptive thermalization; three execution modes including parallel tempering; and HDF5 output that records the configuration, seed, version and commit needed to reproduce a run. Antiferromagnetic and competing couplings, the case most reduced examples get wrong, go through the same tests as the ferromagnet.

Research context. mcising was developed alongside and used in a study of phase determination in the frustrated J1-J2 Ising model with deep learning (Çivitcioğlu, Römer & Honecker, Phys. Rev. E 111, 024131 (2025), arXiv:2403.09786) and its follow-up on minimal training sets (arXiv:2504.19795). The frustration tutorial reproduces the stripe phase of that model, and the examples reproduce Onsager's exact solution and a Binder-cumulant determination of Tc:

Phase diagram of the J1-J2 Ising model on the square lattice: ferromagnetic and stripe order parameters over the (J2, T) plane, with the specific-heat peak line

How mcising compares with peapods, ALPS and the Julia spin-model packages, feature by feature, is on the related work page.

Performance

On one core of an Apple M4 (10 cores: 4 performance + 6 efficiency), mcising performs 351M Metropolis spin updates per second on a 32×32 square lattice at Tc — 140.4× faster than pure Python and 15.0× faster than a NumPy checkerboard implementation of the same update, and 2.4× faster than peapods on a matched workload (energy recorded every sweep on both sides).

mcising 0.29.0 (commit 2e3548a), Python 3.12.11, measured 2026-09-01; medians of repeated runs. Regenerate with uv run --group benchmark python benchmarks/run_all.py --write-docs.

Implementation	Lattice	Timed sweeps	Spin updates/s	mcising is
Pure Python	32×32	200	2M	140.4×
NumPy (checkerboard)	32×32	1,000	23M	15.0×
mcising (Rust)	32×32	10,000	351M	—
NumPy (checkerboard)	128×128	200	69M	4.7×
mcising (Rust)	128×128	1,000	324M	—

Single-spin-flip Metropolis on the square lattice at Tc, one thread, Apple M4 (10 cores: 4 performance + 6 efficiency). Pure Python is a plain loop with precomputed neighbour and Boltzmann tables; the NumPy implementation updates the two checkerboard sublattices as whole arrays. Spin updates/s counts attempted flips; timed sweeps exclude 100 warm-up sweeps.

Matched physics against peapods 0.2.0 (Rust/PyO3): the same Hamiltonian (H = −J Σ s_i s_j, J = 1, energies per site, bond counted once), the same Metropolis sweep (a sequential scan with one attempt per site), the same temperature (Tc), 5,000 thermalization sweeps, then 100,000 timed sweeps with the energy recorded every sweep on both sides, one thread, 3 seeds per side, Apple M4 (10 cores: 4 performance + 6 efficiency). peapods reports +Σ J s_i s_j / N, so its sign is flipped before comparison. A row is published only when the two mean energies agree within 0.5 %.

Lattice	E/site mcising	E/site peapods	Δ	Sweeps/s mcising	Sweeps/s peapods	mcising is
Square 32×32	-1.4325 ± 0.0018	-1.4346 ± 0.0007	0.15 %	249,160	104,786	2.4×
Triangular 32×32	-2.0305 ± 0.0012	-2.0320 ± 0.0014	0.07 %	203,737	86,013	2.4×
Cubic 16×16×16	-1.0346 ± 0.0010	-1.0347 ± 0.0002	0.01 %	34,196	15,677	2.2×

Wolff and Swendsen-Wang are not compared: peapods interleaves cluster updates with Metropolis sweeps rather than running cluster-only sweeps, so no peapods workload matches an mcising cluster sweep.

Every number above is written by benchmarks/run_all.py from the committed benchmarks/results.json, and the test suite fails if the two drift apart. Regenerate with uv run --group benchmark python benchmarks/run_all.py --write-docs (a few minutes), or re-render the committed results with --from-json benchmarks/results.json --write-docs. The performance page adds the per-lattice, cluster-algorithm, scaling and parallel-execution tables.

The two libraries differ in scope more than in speed: mcising has named J2/J3 shells on five lattices including the non-Bravais honeycomb, an external field, quoted statistical errors and provenance-carrying HDF5 output, while peapods covers disordered couplings, spin-glass replica moves and hypercubic lattices in any dimension — see related work.

Features

5 lattice geometries -- square, triangular, honeycomb (2-sublattice), cubic (3D), chain (1D)
3 MC algorithms -- Metropolis, Wolff cluster, Swendsen-Wang cluster
3 execution modes -- sequential cool-down, independent parallel (Rayon), parallel tempering with replica exchange
J1-J2-J3 frustrated magnetism -- nearest, next-nearest, and third-nearest-neighbor couplings
External magnetic field -- h coupling, compatible with all lattices
15 Metropolis strategies -- auto-selected lookup tables optimized per coupling combination
Adaptive thermalization -- MSER equilibration detection + Sokal autocorrelation estimation
Correlation functions -- spin-spin correlation and correlation length
HDF5 output with crash-safe incremental checkpointing
Rich CLI with progress bars, benchmarking, and structured output
Fully reproducible -- deterministic RNG (Xoshiro256**), same seed = same results

Installation

pip install mcising

# with plotting (matplotlib) and/or DataFrame export (pandas):
pip install 'mcising[plot]'
pip install 'mcising[plot,dataframe]'

For development (requires Rust toolchain):

git clone https://github.com/bcivitcioglu/mcising.git
cd mcising
uv sync
uv run maturin develop

Quick Start

Python API

from mcising import Simulation, SimulationConfig, LatticeConfig, LatticeType

config = SimulationConfig(
    lattice=LatticeConfig(size=32, j1=1.0),
    temperatures=(3.0, 2.269, 1.5),
    n_sweeps=1000,
    seed=42,
)

sim = Simulation(config)
results = sim.run()

# Access results per temperature
for T in results.temperatures:
    print(f"T={T:.3f}: <E>={results.energy[T].mean():.4f}, "
          f"<|M|>={abs(results.magnetization[T]).mean():.4f}")

Multiple Lattice Types

from mcising import LatticeType

# Triangular lattice with J1-J2 frustration
config = SimulationConfig(
    lattice=LatticeConfig(
        lattice_type=LatticeType.TRIANGULAR,
        size=32,
        j1=1.0,
        j2=0.5,
    ),
    temperatures=(4.0, 3.641, 2.0),
    n_sweeps=1000,
)

# Also available: HONEYCOMB, CUBIC, CHAIN

Parallel Execution

from mcising import ExecutionMode

# Independent: each temperature runs in parallel (uses all CPU cores)
config = SimulationConfig(
    lattice=LatticeConfig(size=32),
    temperatures=(3.0, 2.5, 2.269, 2.0, 1.5),
    n_sweeps=1000,
    mode=ExecutionMode.INDEPENDENT,  # one temperature per core
)

# Parallel Tempering: parallel + replica swap for better sampling
config = SimulationConfig(
    lattice=LatticeConfig(size=32),
    temperatures=(3.0, 2.5, 2.269, 2.0, 1.5),
    n_sweeps=1000,
    mode=ExecutionMode.PARALLEL_TEMPERING,
)

Adaptive Mode

For large lattices near the critical temperature, enable adaptive measurement to automatically determine thermalization length and measurement spacing:

from mcising import AdaptiveConfig

config = SimulationConfig(
    lattice=LatticeConfig(size=64),
    temperatures=(3.0, 2.269, 1.5),
    adaptive=AdaptiveConfig(enabled=True, min_independent_samples=200),
    seed=42,
)

results = Simulation(config).run()

# Inspect diagnostics
for T in results.temperatures:
    diag = results.adaptive_diagnostics[T]
    print(f"T={T:.3f}: tau_int={diag.tau_int:.1f}, "
          f"interval={diag.measurement_interval}")

CLI

# Basic run
mcising run -L 32 --seed 42 -o results.h5

# Triangular lattice with parallel tempering
mcising run -L 32 --lattice triangular --mode parallel_tempering

# Independent parallel execution (uses all CPU cores)
mcising run -L 32 --mode independent -T 3.0 -T 2.269 -T 1.5

# Adaptive mode
mcising run -L 64 --adaptive --min-samples 200 --seed 42

# With checkpointing (crash-safe)
mcising run -L 32 --checkpoint sim.h5

# Resume interrupted run
mcising run -L 32 --checkpoint sim.h5 --resume

# Benchmark performance across all lattices and algorithms
mcising benchmark

# Show info
mcising info

Saving Results

from mcising import save_hdf5, load_hdf5, save_json_summary

# HDF5 (full data)
save_hdf5(results, "results.h5")
loaded = load_hdf5("results.h5")

# JSON summary (statistics only)
save_json_summary(results, "summary.json")

Examples

Three committed scripts reproduce known physics end to end and write the figures used in the documentation; each runs in well under a minute on a laptop and is executed by the test suite on every pull request:

python examples/onsager_reproduction.py    # <E>/N and <|m|> vs Onsager's and Yang's exact curves
python examples/tc_binder_crossing.py      # Tc from Binder-cumulant crossings of three lattice sizes
python examples/stripe_phase_diagram.py    # J1-J2 phase diagram: ferromagnet vs stripe order

Every script takes --out DIR and --quick; the committed output is in docs/assets/figures/.

Architecture

mcising/
├── rust/src/              # Rust core (compiled to mcising._core)
│   ├── algorithm/         # MC algorithms (Metropolis, Wolff, Swendsen-Wang)
│   ├── autocorrelation.rs # MSER + Sokal windowing
│   ├── lattice/           # Lattice geometries (square, triangular, honeycomb, cubic, chain)
│   ├── observables.rs     # Energy, magnetization, correlation
│   ├── parallel.rs        # Rayon-parallelized execution (independent + parallel tempering)
│   └── simulation.rs      # PyO3 boundary (IsingSimulation)
├── python/mcising/        # Python package
│   ├── simulation.py      # High-level Simulation class
│   ├── config.py          # Frozen dataclass configs
│   ├── io.py              # HDF5/JSON I/O
│   ├── plotting.py        # Matplotlib visualization
│   └── cli.py             # Typer CLI
├── tests/                 # 401 tests (141 Rust + 260 Python)
└── benchmarks/            # Reproducible performance comparisons

How to cite

If mcising contributes to published work, please cite it. The repository's CITATION.cff carries the current version and is what GitHub's "Cite this repository" button renders; a Zenodo DOI is attached at v1.0.0.

A paper describing mcising is being prepared for the Journal of Open Source Software; the draft and its bibliography live under paper/.

@software{mcising,
  author  = {{\c{C}}ivitcio{\u{g}}lu, Burak},
  title   = {mcising: high-performance {Ising} model {Monte Carlo} simulation with a {Rust} core},
  url     = {https://github.com/bcivitcioglu/mcising},
  license = {MIT},
  note    = {Version as installed; see \texttt{mcising.\_\_version\_\_}},
}

If the J1-J2 functionality supported your research, consider also citing the study it was developed for: Çivitcioğlu, Römer & Honecker, Phase determination with and without deep learning, Phys. Rev. E 111, 024131 (2025).

License

This project is licensed under the MIT License.

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mcising 1.0.0

mcising

Why mcising

Performance

Features

Installation

Quick Start

Python API

Multiple Lattice Types

Parallel Execution

Adaptive Mode

CLI

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Examples

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How to cite

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