mcising 0.12

A package for generating Ising model data using Metropolis algorithm on a square lattice for nearest neighbor and next nearest neighbor interactions.

mcising

mcising is a Python package for generating Ising model data using Metropolis algorithm. It works for square lattices, and for nearest neighbor and next nearest neighbor interactions. The Monte-Carlo method it uses, has the cool-down approach to avoid semi stable states.

Installation

You can install the package using pip:

pip install mcising

Usage

You can generate Ising model data from the command line:

generate_ising_data <seed> <lattice_size> <num_configs> <j1> <j2> [--T_init <T_init>] [--T_final <T_final>] [--T_step <T_step>] [--sweep_steps <sweep_steps>] [--thermalization_scans <thermalization_scans>] [--calculate_correlation]

seed: the random seed for reproducibility

lattice_size: the system size L of the square lattice LxL

num_configs: number of configurations to be saved per temperature

j1 and j2: the interaction strengths, j1 for nearest neighbor and j2 for next nearest neighbor

T_init and T_final: initial and final temperatures, initial being higher

T_step: the step in between each temperature point

sweep_steps: number of Monte-Carlo sweeps per step

thermalization_scans: number of sweeps on each temperature step to ensure thermalization

calculate_correlation: option to select if correlation function and correlation length should be calculated, since they are time consuming.

An example usage:

generate_ising_data 42 10 100 1.0 0.5 --T_init 4.0 --T_final 0.1 --T_step 0.05 --sweep_steps 10 --thermalization_scans 5 --calculate_correlation

An example of the output console:

..1 / 11 samples saved.
2 / 11 samples saved.
3 / 11 samples saved.
4 / 11 samples saved.
5 / 11 samples saved.
6 / 11 samples saved.
7 / 11 samples saved.
8 / 11 samples saved.
9 / 11 samples saved.
10 / 11 samples saved.
11 / 11 samples saved.
For temperature= 1.0, MC simulation executed in: 0.43 seconds
.1 / 11 samples saved.
2 / 11 samples saved.
3 / 11 samples saved.
4 / 11 samples saved.
5 / 11 samples saved.
6 / 11 samples saved.
7 / 11 samples saved.
8 / 11 samples saved.
9 / 11 samples saved.
10 / 11 samples saved.
11 / 11 samples saved.
For temperature= 1.0, MC simulation executed in: 0.18 seconds

Example output png files:

Structure of the saved pickle files:

data_sample = {
    'configuration': np.ndarray,  # The lattice configuration (2D array of spins)
    'energy': float,              # The energy of the configuration
    'magnetization': float,       # The magnetization of the configuration
    'correlation_length': float,  # The correlation length (if calculated)
    'correlation_function': np.ndarray,  # The correlation function values (if calculated)
    'distances': np.ndarray       # The distances corresponding to the correlation function values (if calculated)
}

Detailed Description of Each Key

• configuration: A 2D NumPy array representing the lattice configuration, where each element is a spin (-1 or 1).

  • Type: np.ndarray
  • Shape: (lattice_size, lattice_size)

• energy: A float representing the energy of the current lattice configuration.

  • Type: float

• magnetization: A float representing the net magnetization of the current lattice configuration.

  • Type: float

• correlation_length: A float representing the correlation length of the lattice. This is only present if correlation calculations are enabled.

  • Type: float
  • Note: This key is None if correlation calculations are not performed.

• correlation_function: A 1D NumPy array representing the values of the correlation function. This is only present if correlation calculations are enabled.

  • Type: np.ndarray
  • Shape: (num_distances,)
  • Note: This key is None if correlation calculations are not performed.

• distances: A 1D NumPy array representing the distances corresponding to the correlation function values. This is only present if correlation calculations are enabled.

  • Type: np.ndarray
  • Shape: (num_distances,)
  • Note: This key is None if correlation calculations are not performed.

Licence

This project is licensed under the MIT License.