Develop Monte Carlo

Model

Model should contain following fields: lat :: Lattice and rng :: Random.MersenneTwister. Model also should have a constructor taking param :: Parameter as a argument.

You should define convert_parameter for your Model. This is a helper function which takes Model and Parameter and returns arguments of update method and estimator.

@gen_convert_parameter helps you to define convert_parameter. For example, if your model::A needs a scalar T = param["T"] and a vector Js = param["J"] with numbondtypes(model) elements,

@gen_convert_parameter(A, ("T", 1, 1.0), ("J", numbondtypes, 1.0))

defines your documented and type-stable convert_parameter(model::A, param::Parameter) which returns T and Js.

Note:

That the second element of each tuple is not a Function means that a return value is a scalar (the case of "T").
The third element of each tuple is the default value.

"Update method" is a function which (in-place) updates model::Model under some parameters such as temperature T. For example, local_update!(model::Ising, T, Js) updates a spin configuration of model by local spin flip and Metropolice-Hasting algorithm under temperature T and coupling constants Js. "Update method" can return some object which will be used in "Estimator" as extra information.

Example

Swendsen-Wang algorithm SW_update!(::Ising, ::Parameter) returns cluster information sw::SWInfo used in improved_estimator.

Estimator

"Estimator" is a function which returns observables of a configuration model as a Dict{String, Any}. Arguments of a "Estimator" are model::Model, parameters (return of convert_parameter), and extra information (return of "Update method") in order.

Default "Estimator" is determined by model and "Update Method" as return of default_estimator(model, param["Update Method"]).

Example

improved_estimator(model::Ising, T::Real, Js::AbstractArray, sw::SWInfo) takes a return of SW_update!(model::Ising, T::Real, Js::AbstractArray) as the last argument.

Postprocess

postproc(model::Model, param::Parameter, obs::MCObservableSet) is a post process of a Monte Carlo run. Most important objective is to calculate functions of expectation values stored in obs.

For example, "Specific Heat" $C$ can be calculated from "Energy^2" $\langle E^2\rangle \big/ N^2$, "Energy" $\left\langle E\right\rangle \big/ N$, the number of site $N$, and temperature $T$ as $C = \left(N\big/T^2\right)\left[ \left\langle E^2 \right\rangle - \left \langle E \right\rangle^2 \right]$. This is realized as

jk = jackknife(obs)
T = param["T"]
N = numsites(model)
jk["Specific Heat"] = (N/(T*T)) * (jk["Energy^2"] - jk["Energy"]^2)

jackknife converts MCObservableSet (e.g. BinningObservableSet) to JackknifeObservableSet, which enables to calculate functions of mean values and these statistical errors.

postproc returns a MCObservableSet (usually jk::JackknifeObservableSet above), which is also the return value of runMC.