Internal APIs

accumulateObservables!(model, obs::MCObservableSet, localobs::Dict)

Accumulates localobs into obs. For example, obs["Energy"] << localobs["Energy"].

postproc(model::Model, param::Parameter, obs::MCObservableSet)

Post process of observables. For example, Specific heat will be calculated from energy, energy^2, and temperature.

postproc(model::Ising, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $m$ is total magnetization per site and $\epsilon$ is total energy per site.

• "Binder Ratio"

  • \[R := \frac{\left \langle m^4 \right \rangle}{\left \langle m^2 \right\rangle^2}\]

• "Susceptibility"

  • \[\chi := \frac{N}{T}\left(\left\langle m^2\right\rangle\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle m^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

postproc(model::Potts, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $m$ is total magnetization per site and $\epsilon$ is total energy per site.

• "Binder Ratio"

  • \[R := \frac{\left \langle m^4 \right \rangle}{\left \langle m^2 \right\rangle^2}\]

• "Susceptibility"

  • \[\chi := \frac{N}{T}\left(\left\langle m^2\right\rangle\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle m^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

postproc(model::Clock, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $m$ is total magnetization per site and $\epsilon$ is total energy per site.

• "Binder Ratio x"

  • \[\frac{\left \langle m_x^4 \right \rangle}{\left \langle m_x^2 \right\rangle^2}\]

• "Binder Ratio y"

  • \[\frac{\left \langle m_y^4 \right \rangle}{\left \langle m_y^2 \right\rangle^2}\]

• "Binder Ratio"

  • \[\frac{\left \langle |m|^4 \right \rangle}{\left \langle |m|^2 \right\rangle^2}\]

• "Susceptibility x"

  • \[\frac{N}{T}\left(\left\langle m_x^2\right\rangle\right)\]

• "Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle m_y^2\right\rangle\right)\]

• "Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle |m|^2\right\rangle\right)\]

• "Connected Susceptibility x"

  • \[\frac{N}{T}\left(\left\langle m_x^2\right\rangle - \left\langle |m_x| \right\rangle^2\right)\]

• "Connected Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle m_y^2\right\rangle - \left\langle |m_y| \right\rangle^2\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle |m|^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

postproc(model::XY, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $m$ is total magnetization per site and $\epsilon$ is total energy per site.

• "Binder Ratio x"

  • \[\frac{\left \langle m_x^4 \right \rangle}{\left \langle m_x^2 \right\rangle^2}\]

• "Binder Ratio y"

  • \[\frac{\left \langle m_y^4 \right \rangle}{\left \langle m_y^2 \right\rangle^2}\]

• "Binder Ratio"

  • \[\frac{\left \langle |m|^4 \right \rangle}{\left \langle |m|^2 \right\rangle^2}\]

• "Susceptibility x"

  • \[\frac{N}{T}\left(\left\langle m_x^2\right\rangle\right)\]

• "Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle m_y^2\right\rangle\right)\]

• "Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle |m|^2\right\rangle\right)\]

• "Connected Susceptibility x"

  • \[\frac{N}{T}\left(\left\langle m_x^2\right\rangle - \left\langle |m_x| \right\rangle^2\right)\]

• "Connected Susceptibility y"

  • \[\frac{N}{T}\left(\left\langle m_y^2\right\rangle - \left\langle |m_y| \right\rangle^2\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle |m|^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

postproc(model::AshkinTeller, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $m$ is total magnetization per site and $\epsilon$ is total energy per site.

• "Binder Ratio"

  • \[R := \frac{\left \langle m^4 \right \rangle}{\left \langle m^2 \right\rangle^2}\]

• "Susceptibility"

  • \[\chi := \frac{N}{T}\left(\left\langle m^2\right\rangle\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle m^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Binder Ratio sigma"
  • Binder ratio with respct to $\sigma$
• "Susceptibility sigma"
  • Susceptibility with respct to $\sigma$
• "Connected Susceptibility sigma"
  • Connected susceptibility with respct to $\sigma$
• "Binder Ratio tau"
  • Binder ratio with respct to $\tau$
• "Susceptibility tau"
  • Susceptibility with respct to $\tau$
• "Connected Susceptibility tau"
  • Connected susceptibility with respct to $\tau$
• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

postproc(model::QuantumXXZ, param::Parameter, obs::MCObservableSet)

Observables to be calculated

In the following, $s$ is sign of weight, $m$ is total magnetization per site, and $\epsilon$ is total energy per site.

• "Magnetization"

  • \[\left\langle m s\right\rangle\Big/\left\langle s \right\rangle\]

• "|Magnetization|"

  • \[\left\langle |m| s\right\rangle\Big/\left\langle s \right\rangle\]

• "Magnetization^2"

  • \[\left\langle m^2 s\right\rangle\Big/\left\langle s \right\rangle\]

• "Magnetization^4"

  • \[\left\langle m^4 s\right\rangle\Big/\left\langle s \right\rangle\]

• "Energy"

  • \[\left\langle \epsilon s\right\rangle\Big/\left\langle s \right\rangle\]

• "Energy^2"

  • \[\left\langle \epsilon^2 s\right\rangle\Big/\left\langle s \right\rangle\]

• "Binder Ratio"

  • \[\frac{\left \langle m^4 \right \rangle}{\left \langle m^2 \right\rangle^2}\]

• "Susceptibility"

  • \[\frac{N}{T}\left(\left\langle m^2\right\rangle\right)\]

• "Connected Susceptibility"

  • \[\frac{N}{T}\left(\left\langle m^2\right\rangle - \left\langle |m| \right\rangle^2\right)\]

• "Specific Heat"

  • \[\frac{N}{T^2}\left(\left\langle \epsilon^2\right\rangle - \left\langle \epsilon \right\rangle^2\right)\]

generatelattice(param::Parameter)

generates Lattice from Parameter.

numsitetypes(lat::Lattice)
numsitetypes(model::Model)

Returns the number of sitetypes.

numbondtypes(lat::Lattice)
numbondtypes(model::Model)

Returns the number of bondtypes.

makerng(param::Parameter)

Create the random number generator requested by param.

param["RNG"], when present, must be an RNG type, not an RNG instance. It needs only the constructor the other keys call for: T(seed) when param["Seed"] is given, and T() when it is not. Random.RandomDevice and Random.TaskLocalRNG, for instance, provide the latter but not the former, so they work only without "Seed".

When param has both "Seed" and "ID", a child seed is derived for that ID. runMC(params) sets these IDs when autoID=true; runMC(model, param) does not derive child seeds because the model already owns its RNG. That derivation is arithmetic, so "Seed" must be an integer whenever "ID" is present.

childseed(seed::Integer, id::Integer)

Derive a deterministic child seed from an integer seed and an integer ID.

This uses a fixed SplitMix64 finalizer rather than Base.hash, whose values Julia does not promise to keep stable, so derivation reproduces across Julia versions. Child seed derivation is used by makerng(param) only when param has an "ID" key, such as IDs set by runMC(params) with autoID=true. Passing a model directly to runMC(model, param) does not derive a child seed.

Enumtype including LET_*

Loop element depicted as

|
o
|

or matrix

1 1 |+>
1 1 |->

Loop element depicted as

|  |
|--|
|  |

or matrix

1 0 0 0 |++>
0 0 0 0 |+->
0 0 0 0 |-+>
0 0 0 1 |-->

Loop element depicted as

|  |
|~~|
|  |

or matrix

0 0 0 0 |++>
0 1 0 0 |+->
0 0 1 0 |-+>
0 0 0 0 |-->

Loop element depicted as

|  |
~~~~
~~~~
|  |

or matrix

0 0 0 0 |++>
0 1 1 0 |+->
0 1 1 0 |-+>
0 0 0 0 |-->

Loop element depicted as

|  |
 \/
 /\
|  |

or matrix

1 0 0 0 |++>
0 0 1 0 |+->
0 1 0 0 |-+>
0 0 0 1 |-->

(Imaginary-temporary and spatial) local operator as a perturbation with assigned loop element.

Fields

• let_type : assigned loop element
• isdiagonal : operator is diagonal or not
  • in other words, two states connecting this perturbation are equivalent to each other or not.
• time : imaginary time ($\tau/\beta \in [0,1)$) which this perturbation acts on.
• space : spin or bond which this perturbation acts on. denotes space spin if space <= nspins or space - nspins bond otherwise.
• subspace : subspin(s) index
• bottom_id :: index of node of union find assigned to a loop
• top_id :: index of node of union find assigned to the other loop

linear_intercept(xs, ys)

Fit y = a + b*x by unweighted ordinary least squares and return (a, stderror_of_a). The error is a 1-sigma standard error.

Throws ArgumentError if fewer than three points are given, since the standard error needs at least one degree of freedom (dof = n - 2), or if any input is non-finite.

default_estimator(model, updatemethod!)

Determines estimator to be used when param["Estimator"] is not set.

@gen_convert_parameter(model_typename, (keyname, size_fn, default)...)

Generates convert_parameter(model::model_typename, param::Parameter).

Example

@gen_convert_parameter(A, ("A", numbondtypes, 1.0), ("B", 1, 1))

generates a function equivalent to the following:

doc"""
    convert_parameter(model::A, param::Parameter)

# Keynames

- "A": a vector with `numbondtypes(model)` elements (default: 1)
- "B": a scalar (default: 1.0)

"""
function convert_parameter(model::A, param::Parameter)
    ## if `size_fn` is a `Function`,
    ## result is a vector whose size is `size_fn(model)`.
    ## `param["A"]` can take a scalar or a vector.
    a = get(param, "A", 1.0)
    as = zeros(Float64, numbondtypes(model))
    as .= a

    ## otherwise,
    ## result is a scalar.
    b = convert(Int, get(param, "B", 1))

    return as, b
end

Information of clusters in Swendsen-Wang algorithm.

Fields

• activated_bonds : The number of activated (connected) bonds of each cluster.
• clustersize : The number of sites in each cluster.
• clusterspin : Spin variable of each cluster (e.g., 1 or -1 for Ising).
• clustermag : Signed magnetization of each cluster before cluster flips.

Union-find algorithm.

addnode!(u::UnionFind)

Adds a new node into u and returns the number of nodes including the added node.

unify!(u, n1, n2)

Connects n1 and n2 nodes using union by weight and returns the root.

clusterize!(u::UnionFind)

Assigns cluster ID to each node and returns the number of clusters.

clusterid(u::UnionFind, i::Integer)

Returns the index of the cluster where i node belongs.

root!(u::UnionFind, n::Integer)

Returns the root node of the cluster where n belongs. This may changes graph connection by "Path halving" method.

root_path_halving!(u::UnionFind, n::Integer)

Returns the root node of the cluster where n belongs. This may changes graph connection by "Path halving" method.

root_path_splitting!(u::UnionFind, n::Integer)

Returns the root node of the cluster where n belongs. This may changes graph connection by "Path splitting" method.