MCMC-Supercell

Random Perfect Matching MCMC This project implements a Metropolis-Hastings Markov Chain Monte Carlo (MCMC) sampler for generating uniformly random perfect matchings on a lattice graph. The sampler uses a local edge-switch ("flip") move that preserves validity while exploring the space of all matchings. This code was used to generate supercells of A2Se2C2. How it works At each step, the algorithm selects two disjoint matched edges that form a 4-cycle and flips them: (a—b, c—d) ⇄ (a—c, b—d) Because the proposal is symmetric and the target distribution is uniform, every valid move is accepted. The Markov chain is: reversible and satisfies detailed balance ergodic on the space of perfect matchings rejection-free, sampling the uniform distribution This is the standard edge-flip chain uses in random dimer models.