API Documentation

The montecarlo package exposes three top-level classes.

BitString

class montecarlo.BitString(N)

Bases: object

Simple class to implement a configuration of bits.

flip_site(i)

Flip the bit at site i.

integer()

Return the decimal integer corresponding to BitString.

off()

Return number of bits that are off.

on()

Return number of bits that are on.

set_config(s)

Set the config from a list of integers.

set_integer_config(dec)

Convert a decimal integer to binary and set as config.

IsingHamiltonian

class montecarlo.IsingHamiltonian(G: Graph)

Bases: object

Ising Hamiltonian defined on a graph.

H = sum_{(i,j) in E} J_ij s_i s_j + sum_i mu_i s_i

where s_i = +1 if bit i is 1 (up) and s_i = -1 if bit i is 0 (down).

compute_average_values(T: float)

Compute exact thermodynamic averages at temperature T.

Enumerates all 2^N configurations and computes Boltzmann-weighted averages of energy, magnetization, heat capacity, and magnetic susceptibility.

Parameters:

T (float) – Temperature

Returns:

E : average energy M : average magnetization HC : heat capacity MS : magnetic susceptibility

Return type:

tuple of (E, M, HC, MS)

energy(config: BitString)

Compute the energy of a BitString configuration.

Parameters:

config (BitString) – Input spin configuration

Returns:

Energy of the configuration

Return type:

float

set_mu(mus)

Set the local magnetic field terms.

Parameters:

mus (array-like) – Magnetic field values for each site

Returns:

Returns self for chaining

Return type:

self

MonteCarlo

class montecarlo.MonteCarlo(ham: IsingHamiltonian)

Bases: object

Metropolis Monte Carlo sampler for an Ising Hamiltonian.

Parameters:

ham (IsingHamiltonian) – The Hamiltonian to sample

run(T: float, n_samples: int = 1000, n_burn: int = 100)

Run Metropolis Monte Carlo sampling.

For each MC step, sweep over all sites proposing single spin flips. Accept or reject based on the Metropolis criterion:

• If dE <= 0: accept

• If dE > 0: accept with probability exp(-dE/T)

Parameters:

• T (float) – Temperature

• n_samples (int) – Number of samples to collect after burn-in

• n_burn (int) – Number of burn-in sweeps to discard

Returns:

energies : np.ndarray of length n_samples magnetizations : np.ndarray of length n_samples

Return type:

tuple of (energies, magnetizations)