SpinMC.jl

**SpinMC.jl** is a Julia package dedicated to **classical Monte Carlo** simulations of lattice spin models. It offers a straightforward interface for defining custom unit cells and interaction matrices, enabling the study of Heisenberg,…

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Overview

**SpinMC.jl** is a Julia package dedicated to **classical Monte Carlo** simulations of lattice spin models. It offers a straightforward interface for defining custom unit cells and interaction matrices, enabling the study of Heisenberg, XY, Ising, Dzyaloshinskii-Moriya, and Kitaev interactions on arbitrary lattices. It is designed to efficiently calculate thermodynamic properties and identify magnetic phase transitions.

Reference Papers

Reference papers are not yet linked for this code.

Full Documentation

Official Resources

  • Homepage: https://github.com/fbuessen/SpinMC.jl
  • Repository: https://github.com/fbuessen/SpinMC.jl
  • License: MIT License

Overview

SpinMC.jl is a Julia package dedicated to classical Monte Carlo simulations of lattice spin models. It offers a straightforward interface for defining custom unit cells and interaction matrices, enabling the study of Heisenberg, XY, Ising, Dzyaloshinskii-Moriya, and Kitaev interactions on arbitrary lattices. It is designed to efficiently calculate thermodynamic properties and identify magnetic phase transitions.

Scientific domain: Classical Statistical Mechanics, Magnetism Target user community: Researchers studying phase transitions in frustrated magnets

Theoretical Methods

  • Classical Monte Carlo: Sampling of the partition function $Z = \int d\mathbf{S} e^{-\beta H(\mathbf{S})}$.
  • Algorithms:
    • Metropolis-Hastings: Local spin updates.
    • Parallel Tempering (Replica Exchange): Efficient sampling of systems with complex energy landscapes (e.g., spin glasses, frustrated systems) by swapping configurations between different temperatures.
  • Interactions: $H = \sum_{ij} \mathbf{S}i \mathbf{J}{ij} \mathbf{S}_j - \sum_i \mathbf{h} \cdot \mathbf{S}_i$.

Capabilities

  • Model Definition:
    • Arbitrary crystal lattices.
    • Full $3 \times 3$ interaction matrices (generalized exchange).
    • Single-ion anisotropy.
  • Simulation:
    • Thermalization sweeps.
    • Measurement sweeps.
    • MPI-parallelized Replica Exchange.
  • Observables:
    • Internal Energy $E$, Specific Heat $C_v$.
    • Magnetization $M$, Susceptibility $\chi$.
    • Static Structure Factor $S(\mathbf{q})$.
    • Binder Cumulants (for criticality).

Key Strengths

  • Simplicity: Lower barrier to entry than larger frameworks; models are defined in pure Julia scripts.
  • Frustration Friendly: Parallel tempering is built-in, which is essential for getting correct results in frustrated systems like the Kagome antiferromagnet.
  • Julia Scalability: Efficiently scales from a laptop (single core) to a cluster (MPI) without changing code.

Inputs & Outputs

  • Inputs: Julia script with UnitCell, Lattice, and interaction definitions.
  • Outputs:
    • HDF5 files with time-series data.
    • Post-processed binary files with mean/error of observables.

Interfaces & Ecosystem

  • Dependencies: MPI.jl, HDF5.jl.
  • Ecosystem: Can interface with plotting libraries for structure factors.

Performance Characteristics

  • Speed: Comparable to C++ codes for local updates due to Julia's LLVM compilation.
  • Scalability: MPI Parallel Tempering enables simulations of large lattices ($L \sim 100$) near critical points.

Comparison with Other Codes

  • vs. ALPS/MC: ALPS is the classic standard. SpinMC.jl is a modern, lightweight alternative that is easier to modify and integrates better with Julia Workflows.
  • vs. Sunny.jl: Sunny.jl is more general (SU(N) states, dynamics). SpinMC.jl is specifically optimized for classical thermodynamics of dipoles.

Application Areas

  • Spin Liquids: Searching for lack of order in Kitaev/Heisenberg models.
  • Critical Exponents: finite-size scaling analysis of phase transitions.

Community and Support

  • Development: F. Buessen (University of Toronto / KAIST).
  • Source: GitHub.

Verification & Sources

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