Deborah.Esther.SingleCumulant

calc_kurtosis(
    Q1::AbstractArray, 
    Q2::AbstractArray, 
    Q3::AbstractArray, 
    Q4::AbstractArray
) -> Vector{Float64}

Compute the kurtosis of chiral condensate using $Q_1$, $Q_2$, $Q_3$ and $Q_4$ values.

Formula

\[K = \frac{ \left\langle Q_4 \right\rangle - 4 \, \left\langle Q_3 \right\rangle \, \left\langle Q_1 \right\rangle - 3 \, \left\langle Q_2 \right\rangle^2 + 12 \, \left\langle Q_2 \right\rangle \, \left\langle Q_1 \right\rangle^2 - 6 \, \left\langle Q_1 \right\rangle^4 }{\left( \left\langle Q_2 \right\rangle - \left\langle Q_1 \right\rangle^2 \right)^{2}}\]

Arguments

• Q1::AbstractArray: Vector of $Q_1$ values for each bootstrap resample.
• Q2::AbstractArray: Vector of $Q_2$ values for each bootstrap resample.
• Q3::AbstractArray: Vector of $Q_3$ values for each bootstrap resample.
• Q4::AbstractArray: Vector of $Q_4$ values for each bootstrap resample.

Returns

• Vector{Float64}: Kurtosis values per resample.

calc_quark_condensate(
    Q1::AbstractArray, 
    LatVol::Int
) -> Vector{Float64}

Compute the chiral condensate $\left\langle \bar{\psi} \psi \right\rangle$ using $Q_1$ values by normalizing with the lattice volume.

Formula

\[\Sigma = \frac{\left\langle Q_1 \right\rangle}{V}\]

Arguments

• Q1::AbstractArray: Vector of $Q_1$ values for each bootstrap resample.
• LatVol::Int: Lattice volume ($V = N_{S}^3 \times N_{T}$).

Returns

• Vector{Float64}: Quark condensate values per resample, normalized by volume.

calc_skewness(
    Q1::AbstractArray, 
    Q2::AbstractArray, 
    Q3::AbstractArray
) -> Vector{Float64}

Compute the skewness of chiral condensate using $Q_1$, $Q_2$ and $Q_3$ values.

Formula

\[S = \frac{ \left\langle Q_3 \right\rangle - 3 \, \left\langle Q_2 \right\rangle \, \left\langle Q_1 \right\rangle + 2 \, \left\langle Q_1 \right\rangle^3 }{\left( \left\langle Q_2 \right\rangle - \left\langle Q_1 \right\rangle^2 \right)^{\frac{3}{2}}}\]

Arguments

• Q1::AbstractArray: Vector of $Q_1$ values for each bootstrap resample.
• Q2::AbstractArray: Vector of $Q_2$ values for each bootstrap resample.
• Q3::AbstractArray: Vector of $Q_3$ values for each bootstrap resample.

Returns

• Vector{Float64}: Skewness values per resample.

calc_susceptibility(
    Q1::AbstractArray, 
    Q2::AbstractArray, 
    LatVol::Int
) -> Vector{Float64}

Compute the chiral susceptibility using $Q_1$ and $Q_2$ values by normalizing with the lattice volume.

Formula

\[\chi = \frac{\left\langle Q_2 \right\rangle - \left\langle Q_1 \right\rangle^2}{V}\]

Arguments

• Q1::AbstractArray: Vector of $Q_1$ values for each bootstrap resample.
• Q2::AbstractArray: Vector of $Q_2$ values for each bootstrap resample.
• LatVol::Int: Lattice volume ($V = N_{S}^3 \times N_{T}$).

Returns

• Vector{Float64}: Susceptibility values per resample.