# Volume I — Statistical Mechanics & Monte Carlo

Lattice models and the Monte Carlo methods that sample them: the Ising model and
its phase transition, the Metropolis algorithm and detailed balance, the
lattice-gas picture of adsorption, and the kinetic Monte Carlo (residence-time)
algorithm that turns the same moves into real-time dynamics. Each notebook ends
with results checked against exact answers — Onsager's critical temperature, exact
small-lattice enumeration, the ideal-gas limit, the Poisson statistics the
algorithm is built on.

```{admonition} Source lectures
:class: note
This volume develops **Lecture 2** of *Molecular and Materials Modelling*
(FS 2023) — *the 2D Ising model and the foundations of Monte Carlo* — whose
exercise was developed by Dr. Carlo Pignedoli. Each notebook repeats its specific
lecture provenance in its overview; the full lecture map is in `manifest.yml`.
```

```{tableofcontents}
```