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Advanced Usage

Strategies

The Wang-Landau algorithm has rules for determining the histogram flatness and how to update `f. These can be controlled by via keyword arguments flat_strategy and logf_strategy passed to solve.

Histogram flatness criterion

The flatness criterion is defined by FlatHistogramStrategy. The default FlatHistogramStrategy is FractionOfMean which determines flatness by whether the minimum value of the histogram is at least a fraction x of the mean value. Because it is the default strategy, the parameter x can also be supplied directly to solve(prob; kwargs...) with the keyword argument flat_tolerance = x. A custom strat::FlatHistogramStrategy can be passed to the algorithm via solve(prob; flat_strategy = strat).

Implemented flatness strategies include

WangLandau.FractionOfMean — Type
FractionOfMean(tol)

Define the histogram flatness criterion to be when the smallest non-zero value is greater than tol times the mean, which is calculated from states that have at least min visits.

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WangLandau.StableNumVisits — Type
StableNumVisits(min, checksteps)

Define the histogram flatness criterion to be when the number of visited states remains constant for a number of steps checksteps. A state is considered visited if it has been sampled at least minvisits times.

This strategy may be more effective for two-dimensional state spaces (i.e. energy and order parameter), see e.g. Tsai, Wang & Landau, Braz. J. Phys. 38 2008 .

Suggested parameters are min = 2000 and check = N * 10^6 for system size N.

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Density of states parameter $f$

The alteration of $f$ (actually $\log f$) at each iteration is defined by DosIncrementStrategy. The default DosIncrementStrategy is ReduceByFactor which defines a parameter x (default x=0.5) and updates $\log f \to x \log f$ after each flatness iteration. It also defines initial and final values for $\log f$ with defaults 1.0 and 1e-6, respectively. Because it is the default strategy, the final value of $\log f$ can also be supplied directly to solve(prob; kwargs...) with the keyword argument final_logf. A custom strat::DosIncrementStrategy can be passed to the algorithm via solve(prob; logf_strategy = strat).

Implemented $\log f$ strategies include

WangLandau.ReduceByFactor — Type
ReduceByFactor(; kwargs...)

A DosIncrementStrategy to control parameter $\log f$ by multiplying by a constant factor every time a flat histogram occurs, until a desired minimum value is achieved.

Keyword arguments and their default values are:

  • initial = 1.0
  • factor = 0.5: must be less than 1
  • final = 1e-6
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Other features

  • parallelisation (multi-threading): implemented with @atomic. Prior to Julia v.1.12 this requires the Atomix.jl package

  • parallelisation (replica exchange): TBC

  • multi-index histogram/dos: Typically the energy $E$ is a well-defined physical property of the system being studied, but internally WangLandau.jl only treats it as an index to the histogram and density of states. Thus, one could have a system with two parameters of interest, e.g. energy and order parameter. See random_trial!

  • user defined DefType and StateType