Linear aggregation beyond isodesmic symmetry

Exactly solvable models of linear aggregation have been known since Ising's seminal one-dimensional model. This model is defined by a unique nearest-neighbour bond strength that is independent of the length of the cluster; known as isodesmic symmetry. Linear aggregation in real systems has often been associated with broken isodesmic symmetry. Here we show that important examples can be mapped to a class of one-dimensional models that are also exactly solvable.