Concepts

This section is a set of columns: short, self-contained reads that introduce the concepts behind LatticeCore's design. They are written for someone approaching lattice simulation for the first time — or from the software-engineering side — and want to understand why the API is shaped the way it is, not just how to call it.

The goal is not to re-derive condensed-matter physics; it is to make the vocabulary LatticeCore borrows from physics legible, and to show where each concept surfaces in the code.

Where to read first

If you are new to lattices and are here to simulate something, read in order:

1. Lattices and unit cells — what a Bravais lattice is, how unit cells and sublattices work, and why LatticeCore treats the geometric sublattice and the physical site type as independent axes.
2. Reciprocal lattice and Brillouin zone — the dual picture in momentum space. This is the mathematical home of reciprocal_lattice, Monkhorst–Pack meshes, and the structure factor.
3. Boundary conditions — periodic vs open, cylinders, and twisted boundaries, and how each changes the physics of finite-size simulations.
4. Site types and spin models — Ising, Potts, XY, Heisenberg; what the distinction means physically and how LatticeCore represents it.
5. Quasiperiodic order — cut-and-project quasicrystals, Fourier modules, and why the reciprocal lattice becomes dense.

Relation to the rest of the docs