Reference

βc

Critical temperature of the 2-dimensional infinite lattice Ising model determined by Onsager.

binary(s)

Converts to Boolean representation.

dynamic_hybrid!(σ, β; steps, save_interval)

Same as hybrid!, but adjusts numbers of Metropolis and Wolff steps dynamically.

energy(σ, h = 0; f)

Computes the energy of σ in the Ising model.

flip(σ)

Flips a spin.

hybrid!(σ, β; steps = 1, save_interval = length(σ), local_steps = length(σ))

Hybrid sampler, performing local_steps of Metropolis sampling, then one Wolff cluster move, then another local_steps of Metropolis sampling, one more Wolff cluster move, and so on.

kramers_wannier(β)

Returns the Kramers-Wannier dual inverse-temperature of β.

magnetization(σ)

Computes the magnetization of a set of spins.

metropolis!(σ, β, h = 0; steps = 1, save_interval = length(σ))

Performs one or more Metropolis MC steps from the configuration σ, at inverse temperature β. Returns three lists: σ_t, M, E, where σ_t contains configurations sampled at intervals save_interval (by default equals the number of sites), M is the record of magnetizations, and E the record of energies.

mf_energy(σ, h = 0; f = nothing)

mf_random_configurations(N, β, h = 0; f, B = 1)

Generates B random configurations of the Curie-Weiss model.

mf_random_magnetizations(N, β, h = 0; f = nothing, B = 1)

Generates a random magnetization of the Curie-Weiss model, that is, a value of

\[M = \sum_{i=1}^N s_i\]

that follows the statistics of the mean-field (MF) Curie-Weiss model, with energy function:

\[E = -\sum_{i < j} s_i s_j - h * \sum_i s_i + f(M)\]

By default f(M) = 0.

B controls the number of samples generated.

mf_random_magnetized_configuration!(σ, M)

Random configuration with magnetization equal to M.

mf_random_magnetized_configuration(N, M)

Random Curie-Weiss configuration with N spind, with magnetization equal to M.

onsager_heat_capacity(β)

Specific heat capacity of the two-dimensional Ising model, derived by Onsager in the thermodynamic limit.

onsager_internal_energy(β)

Internal energy per site of the two-dimensional Ising model, derived by Onsager in the thermodynamic limit.

onsager_magnetization(β)

Analytical magnetization of the two-dimensional Ising model found by Onsager in the thermodynamic limit.

random_magnetized_configuration!(σ, M)

Generate a random spin configuration with magnetization equal to M. You must make sure that the given value M is feasible.

spin(σ)

Returns +1 or -1 spin value, from a boolean σ representation.

sum_neighbors(σ, i)

Sum of spins in neighbor sites of i.

wolff!(σ, β; steps = 1, save_interval = 1)

Perfoms one or more Wolff MC steps from the configuration σ, at inverse temperature β.