Equilibrium cluster statistics of cooperative and anticooperative binding on finite one-dimensional rings (opens in new tab)

We study equilibrium clustering in a finite one-dimensional lattice gas of $L$ sites with periodic boundary conditions, as a minimal model for adsorption and binding on small ring-like substrates. Using a grand-canonical formulation with nearest-neighbor coupling, we derive exact finite-size expressions for the mean occupancy, the mean number of domain walls, and the mean number of clusters. Building on exact $k$-site correlation functions, we f...