Nchain(N, J0; boundary=nothing)

Create the spin-spin coupling matrix of a 1D chain of N sites with nearest-neighbour interactions of strength set by J0.

Arguments

• N: The number of sites in the chain.
• J0: The nearest-neighbour coupling strength.
• boundary=nothing: (Optional) Specifies the boundary condition of the chain. Default is nothing which corresponds to a chain open at the edges. Use :periodic for periodic boundary conditions.

Returns

An N×N array representing the coupling matrix.

Examples

julia> J = Nchain(4, 2.0)
4×4 Matrix{Float64}:
 0.0  2.0  0.0  0.0
 2.0  0.0  2.0  0.0
 0.0  2.0  0.0  2.0
 0.0  0.0  2.0  0.0

julia> J_periodic = Nchain(4, 2.0; boundary=:periodic)
4×4 Matrix{Float64}:
 0.0  2.0  0.0  2.0
 2.0  0.0  2.0  0.0
 0.0  2.0  0.0  2.0
 2.0  0.0  2.0  0.0

NNlattice(N, Jh, Jv; boundary=nothing)

Create the spin-spin coupling matrix of a NxN 2D lattice with nearest-neighbour interactions and specified horizontal and vertical coupling strengths, Jh and Jv respectively.

Arguments

• N: The size of the lattice (N x N).
• Jh: The horizontal nearest-neighbour coupling strength.
• Jv: The vertical nearest-neighbour coupling strength.
• boundary=nothing: (Optional) Specifies the boundary condition of the lattice. Default is nothing which corresponds to open edges. Use :periodic for periodic boundary condition.

Returns

An N^2×N^2 array representing the coupling matrix of the lattice.

Examples

julia> J = NNlattice(3, 2.0, 1.0)
9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
 0.0  2.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0
 2.0  0.0  2.0  0.0  1.0  0.0  0.0  0.0  0.0
 0.0  2.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0
 1.0  0.0  0.0  0.0  2.0  0.0  1.0  0.0  0.0
 0.0  1.0  0.0  2.0  0.0  2.0  0.0  1.0  0.0
 0.0  0.0  1.0  0.0  2.0  0.0  0.0  0.0  1.0
 0.0  0.0  0.0  1.0  0.0  0.0  0.0  2.0  0.0
 0.0  0.0  0.0  0.0  1.0  0.0  2.0  0.0  2.0
 0.0  0.0  0.0  0.0  0.0  1.0  0.0  2.0  0.0

julia> J_periodic = NNlattice(2, 2.0, 1.0; boundary=:periodic)
9×9 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
 0.0  2.0  2.0  1.0  0.0  0.0  1.0  0.0  0.0
 2.0  0.0  2.0  0.0  1.0  0.0  0.0  1.0  0.0
 2.0  2.0  0.0  0.0  0.0  1.0  0.0  0.0  1.0
 1.0  0.0  0.0  0.0  2.0  2.0  1.0  0.0  0.0
 0.0  1.0  0.0  2.0  0.0  2.0  0.0  1.0  0.0
 0.0  0.0  1.0  2.0  2.0  0.0  0.0  0.0  1.0
 1.0  0.0  0.0  1.0  0.0  0.0  0.0  2.0  2.0
 0.0  1.0  0.0  0.0  1.0  0.0  2.0  0.0  2.0
 0.0  0.0  1.0  0.0  0.0  1.0  2.0  2.0  0.0