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.

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

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).

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.