Visualization

MeanFieldTheories.jl provides built-in visualization through a Makie package extension. Load any Makie backend before calling the plot functions — no other change to your code is needed:

using CairoMakie   # save to file (PNG, PDF, SVG, …)
using GLMakie      # interactive window
using WGLMakie     # Jupyter / Pluto notebook

Lattice Visualization

plot_lattice(lattice; kwargs...) draws a tiled lattice with any number of bond sets and optional sublattice coloring.

Example: Honeycomb lattice

using MeanFieldTheories
using CairoMakie

# Honeycomb primitive vectors and 2-site unit cell
const a1 = [0.0, sqrt(3.0)]
const a2 = [1.5, sqrt(3.0)/2]

unitcell = Lattice(
    [Dof(:cell, 1), Dof(:sub, 2, [:A, :B])],
    [QN(cell=1, sub=1), QN(cell=1, sub=2)],
    [[0.0, 0.0], [1.0, 0.0]];
    vectors = [a1, a2])

lattice = Lattice(unitcell, (4, 4))

nn_bonds  = bonds(lattice, (:p, :p), 1)
nnn_bonds = bonds(lattice, (:p, :p), 2)

fig = plot_lattice(lattice;
    bond_lists   = [nn_bonds, nnn_bonds],
    bond_colors  = [:tomato, :steelblue],
    bond_labels  = ["NN", "NNN"],
    bond_widths  = [1.5, 1.0],
    bond_styles  = [:solid, :dash],
    site_groupby = :sub,
    site_colors  = [:seagreen, :mediumpurple],
    title        = "Honeycomb lattice  (4×4)")

save("lattice_bonds.png", fig)

Magnetization Visualization

plot_spin(mags, positions; kwargs...) encodes the full 3D spin vector in a single top-view panel:

mags is the output of local_spin, and positions is a vector of site coordinates (e.g. unitcell.coordinates). Bond sets produced by bonds can be passed directly to the bonds keyword — no helper function needed.

Case 1 — Square lattice Néel AFM (pure z)

All spins point along ±z; only ⊙/⊗ markers appear, no arrows.

sq_uc = Lattice(
    [Dof(:site, 4)],
    [QN(site=i) for i in 1:4],
    [[0.0,0.0],[1.0,0.0],[0.0,1.0],[1.0,1.0]];
    vectors = [[2.0,0.0],[0.0,2.0]])

sq_NN = bonds(sq_uc, (:p,:p), 1)

mz0 = 0.45
afm_mags = [
    (label=(site=1,), n=1.0, mx=0.0, my=0.0, mz=+mz0, m=mz0, theta_deg=0.0,   phi_deg=0.0),
    (label=(site=2,), n=1.0, mx=0.0, my=0.0, mz=-mz0, m=mz0, theta_deg=180.0, phi_deg=0.0),
    (label=(site=3,), n=1.0, mx=0.0, my=0.0, mz=-mz0, m=mz0, theta_deg=180.0, phi_deg=0.0),
    (label=(site=4,), n=1.0, mx=0.0, my=0.0, mz=+mz0, m=mz0, theta_deg=0.0,   phi_deg=0.0),
]

fig = plot_spin(afm_mags, sq_uc.coordinates;
    title = "Square-lattice Néel AFM  (pure z)",
    bonds = sq_NN)
save("case1_square_afm_z.png", fig)

Case 2 — Triangular lattice 120° Néel order (pure in-plane)

Spins rotate by 120° per sublattice in the xy-plane; only arrows appear, no ⊙/⊗. The magnetic unit cell is the minimal √3×√3 reconstruction (3 sites, one per sublattice).

tri_uc = Lattice(
    [Dof(:site, 3)],
    [QN(site=i) for i in 1:3],
    [[0.0, 0.0], [1.0, 0.0], [0.5, sqrt(3)/2]];
    vectors = [[3/2, sqrt(3)/2], [0.0, sqrt(3)]])

tri_bonds = bonds(tri_uc, (:p,:p), 1)

m0 = 0.45
tri_mags = [
    (label=(site=1,), n=1.0, mx=0.0,             my=+m0,    mz=0.0, ...),  # 90°
    (label=(site=2,), n=1.0, mx=-m0*sqrt(3)/2,   my=-m0/2,  mz=0.0, ...),  # −150°
    (label=(site=3,), n=1.0, mx=+m0*sqrt(3)/2,   my=-m0/2,  mz=0.0, ...),  # −30°
]

fig = plot_spin(tri_mags, tri_uc.coordinates;
    title        = "Triangular-lattice 120° Néel  (pure xy)",
    bonds        = tri_bonds,
    axis_padding = 0.4)
save("case2_triangular_120neel_xy.png", fig)

Case 3 — Canted 120° Néel under uniform magnetic field (all three components)

A uniform field along +z cants all spins by θ = 55° while preserving the 120° in-plane arrangement. Each site shows both ⊙ (uniform positive $m_z$) and an in-plane arrow.

θ_cant = 55 * π / 180
mz_c   = m0 * cos(θ_cant)
mxy_c  = m0 * sin(θ_cant)

cant_mags = [
    (label=(site=1,), n=1.0, mx=0.0,              my=+mxy_c,  mz=mz_c, ...),
    (label=(site=2,), n=1.0, mx=-mxy_c*sqrt(3)/2, my=-mxy_c/2, mz=mz_c, ...),
    (label=(site=3,), n=1.0, mx=+mxy_c*sqrt(3)/2, my=-mxy_c/2, mz=mz_c, ...),
]

fig = plot_spin(cant_mags, tri_uc.coordinates;
    title        = "Triangular-lattice canted 120° Néel  (field ∥ z)",
    bonds        = tri_bonds,
    axis_padding = 0.4)
save("case3_canted_120neel_xyz.png", fig)